Jail Break (Skyrim)

Whiterun
Once you commit a crime in Whiterun and the guards catch you, you can choose to end up in the Dragonsreach Dungeon.

Once you are inside your cell, you are stripped of all your items except for one lockpick. There are two possible ways to escape from the prison. The first one is shorter but much riskier. When you're out of sight of any guards, pick the lock to the main door of your cell (an Adept Level Lock). Then you must search for your equipment.

You can find it in the evidence chest, but watch out as a guard patrols the area. Once you get your equipment, you must carefully escape through the main door, because there are several guards patrolling there as well. The other way of escaping is a lot longer and safer, but it's still not that easy. In your cell there will be a dead bandit lying on the ground. The bandit will be lying on top of a sewer grate with a Novice Level Lock. Open it and you will fall into the sewers.

As you progress you should see a set of stairs leading to a hole in the wall. Through the hole you can pick the lock on the evidence chest and get your things back. Deeper into the dungeon you will see the exit into the guard barracks. Step through and you are free. However, your bounty will still remain. To clear it, simply escape from Whiterun, don't come back for a week, and the guards will eventually forget about you and the bounty will be cleared.

Markarth
See No One Escapes Cidhna Mine article.

After completeing the mission "No One Escapes Cidhna Mine" it is imposible to ever get out without serving your time. (However there is a bug in which you can trap yourself in Cidhna Mine forever by hitting the ore with a pickaxe, you can deplete the silver veins and since the ore dosen't reset after a certain amount of time you will never be able to get the option to serve your time.)

Winterhold
The Chill is rather unique as you get to keep all your stuff even the stolen goods.

First off, after being arrested you are transported very far north, past Septimus Signus's Outpost. Next you'll find yourself in a small cage with one frost atronach acting as a guard.

The cage itself is an adept lock so before you turn yourself in bring lockpicks. Outside are three other frost atronachs and there is a chance to see a Sabre cat depending on your level.