Oblivion:Chameleon

Chameleon is a similar effect to Invisibility. The chameleon effect is not perfect, but it lasts for the entire duration of the effect, regardless of what actions you take. You become more difficult to see at a distance and in light, like a partial invisibility. As you approach 100% chameleon, you become so difficult to see that you can literally steal in front of shopkeepers in broad daylight. Take note that Chameleon does not make you silent: as long as you have less than 100%, creatures and NPCs can still find you, particularly by sound if you have a poor stealth skill or heavy boots. 

The percentage M refers to how well you're hidden. Chameleon actually reduces the range at which you can be detected, rather than the chance of you remaining unnoticed.
Visually, Chameleon will make an actor slowly become more transparent as M increases, vanishing completely at 100%.

100% Chameleon
It is possible to combine multiple Chameleon enchantments to reach 100% Chameleon, causing your character to be visually non-existent and nearly completely undetectable while performing any actions. NPCs will only interact with you if they are scripted to by a current quest or if a guard is attempting to arrest you. Values higher than 100% are possible, but do not provide any additional benefit. With 100% Chameleon, you are able to move freely throughout the game, killing, stealing, sneaking, and doing almost whatever you want without ever being seen or confronted. You are basically invisible to all living creatures or people within the game. However, you can still be damaged by items or traps.

To achieve 100% Chameleon:
Enchant 5 pieces of armor or jewelry with Grand level souls, each with 20% Chameleon.  To do this you must have:
Access to the Arcane University's Enchanting Altars (or the Frostcrag Spire official plug-in).
Access to the Chameleon effect.  The most obvious way is to purchase and be able to cast the standard Chameleon spell, but this requires an  Illusion skill of at least 50.  Alternatively, you can obtain the Fingernail Moon greater power by activating the Shadow Stone.
5 soul gems with Grand level souls (or the equivalent using black soul gems or Azura's Star)
5 items that you want to enchant.  You may want to enchant lightweight or zero weight clothing, since most enemies will no longer detect you to attack; thus, armor rating is no longer important.
Some items found in-game that can be used in place of one custom enchanted item are the Ring of Khajiiti from Meridia's quest (35% Chameleon), or one of several items found in random loot that can provide up to 30% Chameleon.
Alternatively, Sigil Stones can be used to enchant items without requiring access to the enchanting altar.  5 latent Sigil Stones (20% each) provide the same effect as grand soul gems.  Only 4 are necessary with ascendent stones (25%) or transcendent stones (30%).
Custom chameleon potions can be created, up to a maximum strength of 44% for 143 seconds, depending upon your alchemy skill. You can use potions alone or combine potions with a few enchanted items to obtain 100% Chameleon.
It is possible to create a 15 second 100% Chameleon spell once you reach Expert level (75) in Illusion; at Master level, you can make even longer duration spells, limited only by the magicka cost (at Master level, a 60 second spell costs 274 magicka).
Combinations of the above. For instance, the Ring of Khajiiti and two items enchanted with transcendent Sigil Stones gives 95% Chameleon from just three inventory slots. A custom spell can then supply the remaining 5% with a 120 second duration for only 41 magicka.
A long duration 100% Chameleon spell is cast by Volanaro during the Bruma Recommendation Mages Guild quest. It is possible to get the spell cast on your character, as detailed in the quest notes.

Notes
This effect can be gained for spell making and enchanting via spells or the Shadow doomstone or birthsign.
While you can kill a random person right in front of the guards and not be seen, if you try to pickpocket a guard and get caught or talk to one with a bounty on your head they will try to arrest you. However, if you 'resist arrest' you may then be able to simply sneak away, as the guard won't be able to see you to attack.
Attacking with ranged magic can result in being detected in some quests (e.g., the Necromancer's Amulet quest). To become undetected again, leave sneak mode and run somewhere out of sight. The NPCs will go to the position you were at when you left sneak mode, and lose you.
When going to fight in the Arena, the player will be detected once the gates come down. The above suggestion works in order to become undetected once more.
Killing members of a faction you are in will still get you suspended or expelled.
If you summon a creature, or have an NPC following you, they/it will still follow you regardless of your 100% Chameleon.
Magic Traps will still fire at you.
75% to 95% Chameleon instead of 100% Chameleon offers more balanced gameplay.  With low or medium sneak skill it is possible to be spotted, so it is still necessary to play the game tactically.  At expert sneak you become virtually undetectable. You can walk right under people's noses in broad daylight as long as you don't interact with them. Most enemies will find you if you attack though.
If you find it difficult to walk around without seeing your 100% Chameleon character, cast a Chameleon spell upon yourself. When the spell expires, you will become partially visible as if you're not 100% Chameleon.
If you are sneaking when you attack, you will always get a sneak attack bonus with 100% Chameleon.
Interestingly, with 100% Chameleon you will be undetected even when carrying a torch, which is useful at night or in a dark dungeon (even though torches count as a light source and will alter the effectiveness of sneaking).

See also
Sections:
Sneak: Tips on how to sneak effectively

Related effects:
Invisibility
Light

Alchemy Ingredients
The following alchemy ingredients can be used to make a potion of Chameleon: