You should really fill out the following form so that we can help better:
http://www.tomshardware.com/forum/261222-31-build-advice
Specifically, I need to know what peripherals you need like a keyboard/mouse and if you need an operating system. The following, at least, should get you started and we can tweak it depending on some of your specifics. I don't know where people buy computer parts in Europe but google tells me that 900 euros is a little over $1200 USD and I used newegg.com for pricing. I don't know if you need an operating system or a keyboard and mouse on your budget so I left about $100 in the budget.
($300) Monitor: You'll want a quality monitor for gaming. The best graphics card in the world doesn't matter if you have a crappy monitor. The one I picked is pretty expensive, but it's hard to justify going cheaper. If you do go cheaper you'll want to spend the extra money upgrading the HD6950 that I chose to a GTX570. The 23" Samsung PX2370 is a great monitor if you can find it
http://www.newegg.com/Product/Product.aspx?Item=N82E16824001414
($220) CPU: The i5-2500K is the king of the enthusiast gaming world right now. It's almost not even a choice in this price range unless you wanted to go with a $120 CPU (like the i2-2100 or a Phenom II x4) and a more expensive graphics card.
http://www.newegg.com/Product/Product.aspx?Item=N82E16819115072
($125) Motherboard: There is little competition for motherboards in the $125 range. You should pick a mobo that offers x8/x8 SLI mode and arguably the best option right now is the ASRock Extreme3 Gen3. There are options from Gigabyte but the Extreme3 seems to be the most common recommendation.
http://www.newegg.com/Product/Product.aspx?Item=N82E16813157271
($250) Graphics Card: Your GPU is easily the most important part of the build. In your price range a 1GB HD6950 is a really good choice. The Gigabyte model is probably the best price vs. performance option you'll be able to find. If you wanted to spend more on a card you can spend about $350 on a GTX570.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814125385
($85) Hard Drive: I chose a Hitachi 7200RPM 500GB HDD but only because it's cheapest today. With the flooding in Thailand driving up prices you should really just pick whichever ~500GB drive you can find cheapest but make sure it's 7200RPM.
http://www.newegg.com/Product/Product.aspx?Item=N82E16822145299
($29) RAM: For RAM I found the cheapest 2x2GB kit of DDR3, 1600mhz, 1.5V, CAS Latency 9 RAM that I could find from either Corsair, G.Skill, Kingston, or Mushkin. Today that turns out to be a Corsair Vengeance kit but RAM prices fluctuate a lot. As a little side note, if you do go with the Vengeance, make sure you get the low profile version. The high heat spreaders on the regular Vengeance do nothing but get in the way. You'll get arguments that you should get 8GB of RAM, and that's not a bad argument, but there are not many games that use over 4GB. You could go either way, but it's easy enough to get a 2x2GB kit and upgrade later if you find yourself needing more RAM.
http://www.newegg.com/Product/Product.aspx?Item=N82E16820233187
($95) PSU: You'll need a power supply with two 75W 6-pin PCI Express power connectors to power one HD6950. However you might want to leave yourself enough room to power a second one because adding another will be a quick and easy graphics upgrade in the near future. How much power you're going to need depends on how much of an overclock you want. Without knowing that, I'm going to recommend any ~650W PSU from a quality manufacturer. These include Antec, Seasonic, and Corsair. Some people also include PC Power & Cooling or XFX in that list. Getting a modular unit is more expensive, but it will make your life much easier. I chose a 620W Seasonic unit.
http://www.newegg.com/Product/Product.aspx?Item=N82E16817151095
($35) Case: Your case is going to be mostly personal preference. The things you'll want to check, though, is that your case provides decent airflow and that your case has enough room for a long GPU. After those two things you can spend as much or as little as you want. I've linked to three of my favorites: The NZXT Gamma, the Rosewill Challenger, and the Antec Three Hundred.
http://www.newegg.com/Product/Product.aspx?Item=N82E16811146061
http://www.newegg.com/Product/Product.aspx?Item=N82E16811147153
http://www.newegg.com/Product/Product.aspx?Item=N82E16811129066
The above hardware gets you to $1139 USD.
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