(loosely in order by how long ago I first played them)
Chess.
Get xboard
and play on FICS.
Here's a site with lots of
variants.
Scrabble.
Monopoly.
Stratego. Which is actually a good deal of fun once you realize
it's a fast bluffing game and not a deep strategy game. There's an
xstratego for Unix; you want
this version which has a few
fixes relative to the original posted on X.org.
Risk. xfrisk is a free networked
implementation for Unix.