For singleplayer, the Freespace series. Intense, pulse-pounding gameplay, a great and twisting storyline, and, in my opinion, the singularly most frightening enemy of humanity in all of sci-fi. For multiplayer...well, I'm sure you can guess.
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For the non-action type of game, I'd have to say the Myst series; mind-bending puzzles, stunningly beautiful scenery, and intriguing plots all combine to make these games some of the best ever made. Plus, it's the only game series I've seen where the novels are actually good literature in their own right.
P.S. For something on the funnier side, I'd highly recommend Starship Titanic by the late, great Douglas Adams. It's chock-full of Hitchhiker's-type humor. The best part about this game, though, is the robots; you can chat with them by typing in messages, and they'll respond accordingly. Don't think it's all scripted, though; the game featured
16 hours of dialogue, amounting to about
10,000 lines. This thing doesn't get boring.
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