Solo Games

You could try Principal Skinner's suggestion - "see how many envelopes you can lick in an hour, then try to beat that record". Alternatively, I sometimes enjoy patience and crosswords.

Pen and paper games

By far the best group game with pen and paper is Dictionaries (which also requires a decent dictionary). You could also play gops with paper.

Computer games

My favourites are mostly adventure games, because you can play them with other people non-competitively. I have a few arcade favourites too.

Games without equipment

Games without equipment are particularly useful when you are unexpectedly delayed or otherwise bored to the point of desperation. The best I've found are word games like ghost, twenty questions and I love my love - but they all age pretty fast!

Card games

Most competitive card games are so dull that people have to bet on them to stay awake. However, I do like cheat, "up-down" whist, German whist and gops.

Boxed games

(couldn't think of a better title for these - "proper" games?). My top five all-time boxed games based on how often we actually choose to play them are:
  Guillotine (favourite 2-player game)
  Wettstreit der Baumeister (favourite 3/4-player game)
  Trivial Pursuit (fun until we learn the questions)
  Scrabble (when we're awake - hence low position!)
  Pass the Pigs (less fun when sober)
Plus special mentions for Chess, Connect 4, Cheap-Ass Games in general and Ace of Aces.