Oblivion:Under Leveling

Under Leveling is a strategy for dealing with the Leveling Problem; it is one alternative to the Efficient Leveling strategy. In Efficient Leveling you try to gain maximum power when you level by raising your statistics quickly so that you're more powerful than your enemies. With Under Leveling, you try to gain skill points without raising your level so that your opponents do not get more powerful at all.

How to Under Level: 1. Stay Awake

As the Leveling article describes, leveling in the game is something of an "arms race".  Since the game's enemies get stronger as you level up, leveling up can often be a negative instead of a positive; the conventional way to combat this is to use Efficient Leveling, which allows you to maximize the power you gain per level and stay stronger than your foes.

However, efficient leveling isn't the only way to win the arms race.  Not only will much stronger monsters appear everywhere as you gain levels, but at extremely high levels, enemies will start to get stronger faster than you possibly can, since the HP and damage output of many enemies are calculated directly from your level--but your own damage output isn't.

If you never sleep, you will never level up, period.  Even if all your major skills reach 100, you can still remain at level 1 if you want.  So, to minimize the strength of your enemies, you can simply stay at level 1 forever.  That way, your damage output will increase over time as skills like Blade, Blunt, Hand to Hand, and Destruction go up, but your enemies never get stronger in any way.  This gives you a huge advantage over your opponents throughout the game.  For example, with 100 (or even 80) Blade skill and the Honorblade of Chorrol in hand, the vast majority of enemies in the game will die to a single non-power, non-sneak slash at normal difficulty.  

Specific strategies for playing the game without gaining levels:
Complete quests that require sleeping first, before you gain enough major skill points to level up even once.  See Quests that Require Sleep for information on quests that will require you to sleep.
If you wish to remain at level 1 and still join the Dark Brotherhood and Mages Guild, but have already gained ten points in major skills, it is possible to use the Through A Nightmare, Darkly and Where Spirits Have Lease quests to trigger the two required visits from Lucien Lachance without gaining a level, and Vampirism to complete the Anvil Recommendation quest without gaining a level.  You'll be unable to complete the minor quest An Unexpected Voyage, however. (This is not correct as you can avoid leveling up by sleeping for 1 hour and cancelling directly before the hour changes. Example: 
Since you won't really be using trainers to raise your skills, it's especially important to know how to manually increase your skills efficiently.  See Increasing Skills for more information.
Use what little training you're allowed to do to raise your highest skills, since they take much longer to raise manually.
Use the Enchanting altars to create equipment that boosts your relatively weak attributes using the Fortify Attribute effect.

Much of the equipment in the game is leveled, and at level 1 you'll be hard-pressed to find equipment better than Silver weapons and Steel/Chain armor.  However, there are still some very nice non-leveled weapons to be found:

The aforementioned Honorblade of Chorrol is relatively easy to obtain, and at level 1 is far more powerful than most other weapons you'll find.  See the Separated at Birth questline for information on how to get it.
The even more powerful Umbra is one of the game's best swords regardless of your level, and can also be obtained at level 1.  However, unlike the Honorblade of Chorrol, it is much more difficult to obtain, as you must defeat a level 50 opponent to get it.  It can be done, however; see this page for some strategies.
There aren't really any blunt weapons comparable in power to the above two that you can get at level 1.  If you plan to use this strategy, Blade is probably a better main weapon choice than Blunt for that reason alone.
For armor, the set of Elven armor that Azani Blackheart wears is quite a bit better than most armor available at low levels.  There's also the set of Ebony armor that Umbra wears, but again, that's much harder to get.

Note that the only quests that are fully impossible to complete while remaining at level 1 (without the console) are fourteen of the fifteen Daedric shrine quests (Clavicus Vile can be completed, and therefore so can the main quest) and Marksman Training, though the latter can be "completed" by killing the trainer.  That still leaves 185 out of the 199 completable quests in the game for you to do, all without gaining a single level.  Of course, you can always level to 2 if you want to make the main quest a bit easier and avoid Umbra (you can do either Azura's quest or Sheogorath's quest at level 2).

How to Under Level : 2. Play against the majors

This is a technique for people who want to finish the Main Quest at level 2, or play the entire game at 100% difficulty, or just don't like the arms race and always want to have an edge over their opponents.  The principle is simple:  choose major skills that will not be used and can be controlled. For example if the character is to be melee-averse try this set of seven majors: Block, Hand-to-Hand, Blunt, Armorer, Mysticism, Marksman, and Heavy Armor. The specialization could be either stealth or magic, but not combat. While the actually used skills continue to advance and acquire perks, the monsters wait patiently at level one, until the character deems it time for them to move up.

Playing against the majors, may still be possible even if the character was not created with that intent. The question would be,  "Can the 14 minor skills make a viable character and are the majors controllable skills?" Additionally, this strategy generally assures +5's in the appropriate governing attributes at the lower levels once the decision to use the majors enough to level up is made. Also, be careful not to read skill books that are potentially going to advance a major skill.

Advantages
Remaining at level 1 means that your Attributes will never increase, except with enchantments and spells. In this way, you must carefully choose your race, birthsign, and Attribute bonuses. When max leveling, it doesn't matter what you start with because all characters can get their Attributes to 100 and therefore all characters are essentially the same (save for Endurance, whose base level actually matters). This is not the case with under leveling. By staying at a low level, you do not make obsolete your race's Greater Power (like Ancestor Guardian or Beast Tongue) and unless you are specifically a mage character, you will probably not be able to gain enough Magicka to simply cast spells which could otherwise be obtained as birthsign Powers (Moonshadow becomes particularly useful in this scenario). This focus on character creation and limit on the strength of your character adds a much more RPG feel to the game.

Disadvantages
Most loot and quest rewards level as well, so under either strategy, you will never receive the highest level of quest rewards or see daedric armor or weapons. This particularly applies to enchanting with Sigil Stones. See Advantages of Leveling.
It may be slow going at first until a few key minor skills hit the Apprentice level, which is where they would have started as majors.
It may be difficult to put together efficient 15 point level ups at higher levels since the needed minors may be maxed out.
You will need to use the five skill training points carefully since there will be significantly fewer level ups.
It might get a bit boring fighting against Stunted Scamps, Imps, and vanilla Skeletons nonstop.  The game's monsters have far, far less variety at low levels.
You'll basically be stuck with whatever attributes you start with; if you decide to enchant your equipment to raise them, then that means you can't use your equipment for other useful enchantments.

Other Strategies
Oblivion allows you to level as much or as little as you please, so if you find yourself getting bored with being level 1, but don't want to ruin the experience by making yourself a maxed out super soldier, you can consider only leveling up to a predetermined level. For example, you could create a warrior, starting the game with 65 Strength and Endurance and only level until those Attributes reach 100 (which will be done by level 8 if you level efficiently). This leaves one Attribute each level for you to raise at your discretion. In doing this, you can focus only on the Attributes you find useful to your particular character, meaning you can enjoy the benefits of leveling up while still retaining a conventional RPG experience.