Elder Scrolls IV: Oblivion Tips & Tricks

If you go right outside the north gate of Anvil, you will see a stable called "Horse Whisperer". If you go and hop on one of the horses that is considered stealing, and you will be arreasted. But, if you hop on and ride away in a flash the foot soldiers will not be able to catch you. There are a few mounted but you can ride past them. You will be wanted though so be careful.

In the caverns in the game's intro, once you get into the large room with three or four goblins in it, kill the one to your immediate left. Then, go into sneak mode and sneak along the wall to the right of the way you came in. There will be a spot that will "catch" your character but he will continue to move in place. Set the analog stick on something so it will hold itself, leave the room for a while, and then continue the quest once you reach the sneak level you want.