There are many games you can play depending on what you are interested in..
1.Entropia Universe is very famous among "galactic" games. Abt 750.000 ppl are playing it
2.Richard Garriot's Tabula Rasa is a game that is considered to be the ancestor of MMORPG's whilst it has many bugs and it is still developing but it is playable of course.
3.Eve Online is another "Galactic" game which takes place in a huge universe.Note that skills are trained in real-time so you can train a skill even if you log-out.
4.There is a game called Dungeon Runners which is idiotically funny.You should try it if you like games like Diablo.
5.If you like Dungeons and Dragons there is an online version of that (Dungeons and Dragons online) but it is not very famous and I wouldnt reccomend it either...
6.On the other hand I would reccomend City of Heroes/City of Villains.
That game is something different than the other MMORPGs. You are a superhero fighting supervillains flying, doing stuff like in comic books.
There is an impressively large variety of customization to your character and powers and the gameplay is also good...
7.There is also Warhammer online.
8.Finallly you can play some of the most famous MMORPG's online on free servers.All you need to do is google

Games like Warld of Warcraft, Linage(I dont reccomend), Age of Conan and Lord Of The Rings Online can be played in free/non-official servers so you dont have to pay 15 euros/month.
Thats all!
Also dont get stuck with a MMORPG.They are good but real life is better. And for god's sake dont play Second Life..Its ridiculous.
Hope this helps