I believe most in-game areas reset after a certain amount of time in-game. There are mods out there that increase and decrease the length of time that cells wait in between each reset.
The only exceptions I would believe are storage containers in houses that you as a player own. Of course, you're not about to rob yourself, are you?
If you want to add a touch to thievery in Oblivion, I can suggest a couple mods for the PC version.
Oscuro's Oblivion Overhaul - Disables scaled leveling, makes the game more of a challenge, and keeps your average low life bandits from acquiring glass armor from thin air.
Thievery in the Imperial City - Adds a second thievery storyline, so you don't have to resort to the Thieves Guild. It isn't completed I don't think, but it provides a nice storyline, with a fence that isn't associated with the Thieves Guild.
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Formerly NWC_Omega