Based on your bounty and/or notoriety-so committing a few minor crimes in one place will only get you in trouble with the guards in that location-and they might even forget about you after awhile (only if your bounty is exceptionally low). Committing a major crime like murder or stealing something particularly valuable will get you in big trouble in the place where the crime was committed and over time word will spread across Skyrim until eventually you're a wanted man/woman everywhere.
I can also imagine that once you rack up a high enough bounty you may even have mercenaries/vigilantes coming after you to collect the price on your head.
There still might be an option to remove bounties via special NPCs in the Thieves/Assassins guilds-although there could be limitations on that as well-perhaps based on how much "influence" the particular NPC has. You might also be able to "turn yourself in" to any guard anywhere, but again just talking to a guard in another city won't get you in trouble-you'd actually have to select the topic to turn yourself in rather than the guard automatically recognizing you as a criminal.
As far as stolen goods are concerned, there's been discussion about it in the thread I mentioned so I'll only cover it in terms of how it related to the guards. They shouldn't be able to recognize every little item you've stolen-so in terms of what they confiscate it may be limited to the following;
- The item(s) they saw you steal.
- Possibly any locally stolen item(s) past a certain value and after a certain period of time after you've stolen them (during which they were "reported" as stolen to the guards).
- Any unique or rare item(s) that clearly don't belong to you.
Any minor or common items that were stolen may not be confiscated. Also, if there's an element of "notoriety", the guards may be more suspicious-perhaps even to the point where they'll confiscate certain items you did not steal (or maybe not-I think it could be a nice little touch) that they think are suspicious. It's possible they might return them to you later or something. You can still retrieve your items by lockpicking the "evidence chest" .
I do have some hope that we'll be able to see at least some of this thanks to the Radiant Story system.