Make sure to check out Yucata.de too. They have about 200 games with some overlaps with BGA. The site UI takes some getting used to and matchmaking is not as well featured as BGA's but the in-game UI is actually very nice once you grok it and it has an excellent undo/replay/log system.
Some of my Yucata favorites:
- Bonfire
- Carpe Diem
- Cartographers (also on BGA)
- Fields of Arle
- Grand Austria Hotel
- Lorenzo Il Magnifico
- Mottainai
- Mountain Goats (also on BGA)
- Mystic Vale
- Newton
- Rajas of the Ganges
- Rajas Dice
- Red Cathedral
- Renature
- Taverns of Tiefenthal
And I am currently practicing Skymines.