Since a lot of people are asking "If I buy there, do I get a cut version?", I think I should make a thread about it and answer the most asked questions about it. Feel free to ask things or share your experiences with issues. Also note that information in this thread probably doesn't match all games and situations, there are always exceptions.

I have a STEAM-gift. Is it a low violence version?

Most Steam gifts aren't low violence versions since publishers cut their games almost only for Germany and Australia. Steam makes it easy for you: A low violence has a special tag: (DE), (LV) or (AU). If you see it you have a low violence version.
Look here

I have a key. Is it a low violence version?

You can't know that from looking on 15 random letters/numbers, duh. Fortunaly most shops tell you what kind of key you are buying. Search the game at SteamDB (look below). Note that German shops obviously sell cut versions.
Also you can find it out afterwards, by clicking here. If the game in that list has a (DE), (LV) or (AU) tag, you got an low violence version. Other tags have nothing to do with cuts.
Look here

So, how can I get an uncut version?

a) Trade! Look out on the major trading sites and try to get a gift of the game you want. Most traders want keys for it. But always beware of scammers and only trade inside the trading window.
Major trading sites are:

• Steamtrades
• TF2 Outpost
• Bazaar.tf
• Reddit
• SteamExchange

b) Buy a key from authorized resellers. These must tell you like Steam if their games are cut. Some authorized resellers are:

• Green Man Gaming
• Gamersgate
• Nuuvem
• Amazon.com
• Gamefly
• GetGamesGo

Note that some publishers (e.g. Activision, THQ) block keys for Germany, so make sure that the version can be activated!

Don't try to use VPN to buy from another regions Steam store.

Make sure that the copy runs in your country, some games are cheap, but only run in a few countries.

You can check that over at SteamDB if you know where your trader lives or what kind of copy you'll get. Just search for your game, then click on the version, that you want to buy. A quick example: after searching "Skyrim" I chose the Russian copy of Skyrim. A new site opens and there I can see this. As you can see there is a line called "onlyallowrunincountries". If your country isn't in there, you can't run it! If there is no line, there is no restriction on it.

Another thing is the activation of keys: Note that a few of the resellers (I'm looking at you, getloadedgo) tend to have no clue or are just unaware of that issue, so I suggest you to check these SteamDB entries as well. Why? Well,
(1) some shops just say "not for Germany", but if you buy there with (or even without) an fake adress you just get an uncut key as well (which is obviously good for you) or
(2) the shop says nothing about locks, but the publisher has locked the keys. (Often hapens when buying from Russia)
Now back to SteamDB: Let's take CoD: Black Ops Retail as an example: This key has "PurchaseRestrictedCountries". If you are in there, you are blocked. Write a "Thank you!"-letter to the publisher. If there is no version with region restrictions then you are fine.
Note that this information applys to all kind of region restrictions as well.

Is it bad to bypass the restrictions like that? Will Steam ban me if they find out that I play games without grey blood?

No, Steam doesn't care about that.

It's too late. I found out that I have a low violence version. So, how bad are the cuts? / Is there a cut version of this game?

Very easy, if you speak German. Click the link below and search for the game. Then read the article about it. If you don't speak German, I suggest you to use a translator, but most of the times you can see the most important things from the images.

Schnittberichte.com

Also you can try out Movie-censorship.com (thanks to TheEternalComedian). Please note that it seems like this site misses some entries, so make sure to double-check with schnittberichte.com.
I really want an uncut game, but I already have the cut version in my account and Steam tells me, that I already own the game. What to do?

Contact Steam support. Ask them to remove the cut version from your account. Do what they want and activate your game afterwards.

I'm not from Germany or Australia, but I got a low violence version. Can Steam support help me out?

This depends on the support staff. I have heard that they changed the version of game and I've heard that they did not do this as well. But it's worth a try, I guess.
Note: If the game is cut in your region as well, Steam support refuses to change the version of course.

I'm in the Familiy Sharing Beta. My friend/family member shared a game with me. How does it work?

If somebody shares a cut game, the game remains cut. If someone shares an uncut game, the game remains uncut. If a shared game is not available in your region (no store page), you can still play it. If a game is region locked in your country, it remains region locked if you are not in the required region.

This may change during the Family Sharing beta, this information is from 27/09/2013.

I accidentally closed my old topic, it can be found here