Skyrim:Roleplaying

Roleplaying is an optional way of playing the game, that can range from a brief diversion to a full overhaul of the game.  By playing as if your character has a personality and preferences beyond the game's basic statistics, you can add additional depth and interest.  At a basic level, many players will give their characters some sort of backstory explaining who the character is.  Beyond that, you can choose to incorporate limitations that make gameplay more realistic or more challenging, as detailed in Increased Realism.  Or you can model your character after any favorite person, real or fictional.

Increased Realism
There are a wide variety of ideas for how to make the game more realistic, that can be used alone or combined based upon your preferences. PC players and Xbox/Playstation players with Special Edition can enhance many of these ideas by adding various third-party mods. 

Traveling
Slow down! You don't need to run/jump everywhere. Take a walk in the forests.
If you do run while you travel, take the occasional rest.
Only travel in good weather. If you must travel in poor weather, wear appropriate attire. Consider running to find a camp or cave to wait out the storm.
If you come across a village, don't keep going. Unless you're doing something important, stop by. See how the livestock and townspeople are doing.
Spend nights in inns or taverns.  If you are caught in the wilderness at night, stop by the side of the road as if you were camping for the night.
Stop and pray at chapels during your travels.
For players who consider Fast Travel to be unrealistic, its use can be minimized or eliminated.  Spending more time journeying across Skyrim can greatly enhance the aesthetic appeal of the game; some of the lesser travelled places are stunningly beautiful.
If going everywhere by foot or horse is too tiresome, remember to make use of Skyrim's transport services such as carriage drivers!
Use your map and compass more realistically
Use your map only when you are sheltered. If it is raining or snowing, your map could get soaked and most likely ruined.
When entering a dungeon, carry a torch and walk slowly, on the lookout for unknown dangers.

Horses
Take care of your horse more realistically.
Always leave your horse at a stable, in its paddock.
Leave an apple or carrot near your horse.
Chat with the proprietor and tell them to take extra good care of your horse.
When riding, take your horse's stamina and Health into account.
Don't run nonstop between cities through the middle of the wilderness, jumping over boulders, running into trees, and swimming across lakes. When possible, stick to the roads.
Only run full speed when you are attacked or urgently need to get somewhere. Slow down when your horse is exhausted or injured.

Eating
Although it is not necessary, eating regularly is an easy way to enhance roleplaying.
Eat three meals a day at the appropriate times (or fewer if you are poor).  Eat foods appropriate for your character and the mealtime.
Once you have eaten, wait for one hour to show it takes time to actually eat--you haven't just instantly eaten your meal.
If you find yourself a long way away from a house or an inn, then gather some nearby natural ingredients. Seeds, flowers and other things could make a meal.
Sit down in a chair when you eat.
Eat out at the local inn, socializing with others. 
If you had a particularly good meal at an inn, tip the barman by bribing him.
If you have access to a camp fire or similar, make sure to make good use of it. No sense in eating raw food when you can cook it!

Sleeping
Sleep in a home appropriate for your role.  If you can't afford a house (or do not want one), rent a room at an inn or find a bedroll.  Also, rent a room when you are visiting a city.
Put your armor in the cupboards or on mannequins, put your sword on the bed next to you, etc, before you sleep. Put on a simple outfit as "pajamas".
Read a book before going to bed, like you fell asleep reading.
If you must wait instead of sleeping then wait under a balcony or a tree, or in a crevice in a wall, to simulate sleeping on the streets or wilderness.

Houses
Take off your shoes when you enter your house.
There are many options for decorating your house:
Place appropriate items throughout: books on bookshelves, wine in wine racks, decorative armor on shelves or mannequins, writing items on desks, food and dishes in the kitchen. If you are a mage put potions and scrolls everywhere. If you own a nice home (Hjerim, Proudspire Manor, Vlindrel Hall etc.) put expensive drinks on shelves as most nobles do.
Create displays that commemorate your adventures, for example by showcasing items representing animals or people you have conquered: a mammoth tusk in a display case or a Daedric Artifact on a shelf.
Flag your storage chests to give you a hint as to what they contain. Leave your favorite weapon atop your weapons chest, a pickaxe over the crate where you keep your ores or dungeon delving trophies, etc.
Have a butler in the manors. Get a follower and tell him/her to wait by the door and greet you when you come home. If you have a house from Hearthfire you can hire some followers to become personal stewards.

Equipment
Try playing the game using a realistic limit for the amount of items your character can carry.  If you need to transport more items than a person could realistically carry, use a horse.
Wear clothing appropriate to the weather and/or activity. Keep that fur armor handy for trips to the northern areas of Skyrim.
Take off your armor and replace it with casual clothes when you're in towns. If you use a shield in combat, equip a two-handed weapon or a bow when in towns so that you can use both hands without your shield getting in the way.
Wear clothing and use weapons that are appropriate for your character.
When doing quests for a particular faction, try wearing the armor that faction gives you, such as wearing your Wolf Armor for the Companions, or your Shrouded Armor for Dark Brotherhood quests.
:* If you're roleplaying a character who is especially loyal to a given faction, such as the Imperial Legion (see the section on "Character type roleplaying" for more details), consider wearing that armor even when you're out adventuring on your own.

Combat
Simulate damage from combat beyond simply losing health. 
Rest after a fight so you are prepared for your next encounter. 
After a major battle or after catching a disease, take several days to gradually heal, slowly doing more physically demanding activities. 
When your health drops below a certain level, flee from the battle, preferably to the nearest town and seek help from the guards (however, make sure the guards can actually defeat your enemies).
Don't change armor after combat has begun.

Memorials
If you become attached to the NPCs in the game, you can pay homage to them after they die.
Place the NPC's robes/armor and/or sword in a place of significance and honor.
Rename the items (by enchanting them, for example) to name them after the NPC who used them.
Conduct a memorial ceremony, for example by shooting a flame arrow or a spell into the sky.
Scatter flowers and torches where someone died.
Use the weapons, armor, or spells of fallen NPCs when avenging their death.
Straighten out a fallen ally's (or opponent's) body (folding the arms if possible) and place the body in a peaceful location. If he or she died in the water, drag the corpse onto land, possibly a meadow of flowers, and perhaps leave a flower next to the body.
If near a fire, cremate the body by dragging it in.

You can also honor your fallen enemies, in particular if they fought honorably. This may include people acting immaturely, they didn't mean or want to start combat.
Take their armor only to upgrade your own, not for profit.
Leave their weapon next to their body to symbolize that they died honorably.
If someone such as a Dark Brotherhood Follower dies, hide the corpse and clothes so no one can learn anything of the Dark Brotherhood's enchanted armor.

Religion
Dedicate your life to a Daedric Prince or God. Choose a god to follow based on your character's race and class.
Worship your Chosen god through activities that would please your particular god. Visit the chapel every morning and pray.  If you strongly believe in your god then you could wake up every day at a certain time and place a gift on the altar. Place fresh flowers on graves to show the gods that you're devoted to them.
Worship according to your race if you hold pride in it. For example as a Khajiit, worship the Khajiit pantheon and drink Skooma to make you feel closer to the Lunar Lattice. This can be changed depending on what race your character is.
Summon a Dremora Lord only on certain days. You could therefore celebrate these days by acting as a madman on Sheogorath's summoning day, reading books all day when it's the summoning day of Hermaeus Mora, etc.
Read through and study the holy texts of your religion. Copy them and drop them in public places to spread your faith!

Family

If you have a family, keep in touch with them, or create a scenario that discourages contact.
If they died, that may change your opinion about the races, factions, or people involved.
If your parents or close family are rich or powerful, then you have great power where they live. In other words, if your brother was a Jarl, you would have much influence.
If you are part of a noble family like the Battle-Borns, throw your newfound power around. Also, enchant your gear and name it after your family.
Make your family race-appropriate so no Altmer fathers and Orc children.
When developing your family tree, remember that, according to the lore book Racial Phylogeny, the race of the offspring is determined entirely by the race of the mother, while the father only bestows minor traits such as eye/hair color or how pointy the ears are. Bear this in mind when developing a family tree; remember that your father can still be any race you want; just that your mother has to be the same race as you and all your siblings.
It is also speculated that the father may also pass on minor racial traits onto his offspring, such as an aptitude for magic, which is believed to be how the Bretons came to be. Thus, giving yourself a Nord mother and an Altmer/Breton father could be used to explain how your Nord character has an uncanny knack for learning magic, something Nords usually frown upon.
Play with a race that has few last names, like Altmer. Other Altmer that you like, or even dislike, for drama, are your relatives.

Miscellaneous
Give your character a personality with preferred foods, activities, and clothes.  What creature or race does he/she hate/like the most? 
Observe a certain code befitting your character's morality.  For example, if you prefer to play as someone honorable, take only the loot that compensates you for the potions and soul gems used to heal your wounds and recharge your weapons (think of this as the equivalent of "compensation for injuries"), and even then, only if they picked the fight with you.  If you're visiting bandits for a quest (in other words, you're the one picking the fight), take only what you came for, and nothing more.
Do not reload your last save game after making a mistake, such as killing someone accidentally. Continue playing and live with the consequences of the mistake.
Adjust the difficulty slider based on your game-play preferences.
 With a very basic view of the Creation Kit, you can make your own people and add them to the world of Skyrim (workers, family, etc.).
Given that most people don't have supernatural attention spans, try not to wait for long periods of time all at once, unless there is a good reason (e.g., you're spying on someone).
Bathe periodically by taking off your clothes and swimming.  Wash your clothes, too, by dropping them in the water. For more realism, drop them in a sunny place and wait for them to dry; if it's cloudy, wait a bit longer.
Take a trip to the excellent bathing areas in the warm springs of southern Eastmarch (surrounding Bonestrewn Crest).
Never bathe in frigid northern waters unless you have a really good reason and there is plenty of warmth and shelter nearby.
Choose a date to be your birthday and celebrate it.
Read The Firmament and find the appropriate Standing Stone to match your birthday.
Use Followers as bodyguards, friends or colleagues.
Tell your followers to wait in a place where they would actually stay (Inn, bar, guild hall etc.)
Put a realistic limit on how much gear can go into a container. How can you put seven sets of armor a war axe and six tower shields into one chest? Take the size of the item into context, a staff cannot be put into a lectern but maybe in your hunting closet. Also your desk should not contain weapons and armor even if it would fit. Inkwells, books, and maybe a dagger is good though.
Play the game according to your chosen race:
Try to only use skills that your race favors (e.g., skills for which your race has positive modifiers).
Only deal with merchants of your race; generally try to help NPCs of your race.
Use appropriate equipment (Orcs use Orcish; Elves use Elven; etc.)
If you are role-playing a job for which you should be paid, you can receive your pay in multiple ways:
Pickpocket your pay from the person you're dealing with.
  On the PC you can also use the console to collect your pay.
Use a War-Hammer or similar weapon when entering taverns or other places you'd like to be noticed.

Character Type Roleplaying
General Character Creation
You can create and develop your character to emulate any person you like, including heroes from stories and movies.  There are several basic ways you can customize your character to resemble your rolemodel:
Give your character a race appropriate name.
Choose an appropriate race and gender.
Customize your character's appearance to match your rolemodel.
Equip your character with appropriate clothing, armor, and weapons.  Enchant items to rename them.
Decide which NPCs are your friends and which are your enemies.  Only do quests for your friends, and only join guilds that are appropriate for your character.
Create a backstory for your character.  Have the character learn lessons from their backstory, and apply these life lessons to their actions in-game.

You don't necessarily have to start a new character, although your options are more limited if you are building on an existing character.