Damn, this is tough. I'm trying to focus on games that I know a lot of EoFFers haven't already played.

The Longest Journey & Dreamfall, because when it comes to quality vs. popularity they are enormously underrated. Also, the final in the trilogy, Dreamfall Chapters, is in production and should be out by the end of next year.
Dwarf Fortress, because everyone should get to grips with this so we can have more DF LP's.
The Mark of Kri, for similar reasons to TLJ & Dreamfall.
EVE Online, only because I really, really want to get into it but I don't want to do it without a lot of good friends to enjoy it with. Danielle and I tried a one month free trial ages ago but if you don't have a lot of friends then MMO's just aren't fun at all. Thankfully Star Citizen will come out and satisfy my hunger for space.