RavenBlack, the Player of Games.
Here, some categorised games...
Strange time-filling games
Word Dissociation (can be played alone)
Psychological Ju-Jitsu
Elementals
Ghost, Spook and other variants.
Board/Paper/Email games
Unorthobox - a paper/email game for two players
Logi-Sticks - a board game for two to four players
Bees! - a hex-board game for two players
Card games
Cheat - a game usually for more than two players
Splat - a game usually for only two players
Online games
Vampires - a web-based massively-multiplayer game.
Warlocks - a web-based multi-player game, running on this very server. Join, play!
Firetop Mountain - the email-based game Warlocks was based on (or copied from).
AbsoluteMUSH
Scrabule (A lot like a word game of a similar name, but played on a MUSH.)
Treasure Hiding - an email game for two players.
Multi-player computer games
Warcraft 2 - my favourite competitive computer game. Why is everything newer so bad?
Single-player computer games I recommend (a mix of especially good, or good and not well known)
Ultima 4, 5, 6, Ultima Underworld and Ultima Underworld 2 from Origin, and the Exile series from Spiderweb Software, are all very good in the RPG genre, and probably a pain to run on modern computers. Spiderweb Software's later things are also pretty good, but not as good as their older stuff.
Beret is a unique, free puzzle platformer involving telekinesis.
Wonderquest Dreams is a good free variant on Deadly Rooms of Death. The download link is tricky to find, search the linked page for "WonderQuest_Dreams_Setup_42.exe" and it's the second one in the left column under "RabidChild".
Iji is a free metroidvania that can be played at least two very distinct ways that lead to different endings.
An Untitled Story is a lo-fi free metroidvania. (Mouse over the game images to see their titles.)
Cave Story is a very cute metroidvania made by one guy.
Miracle Fly is a really good cross between Super Mario and Thrust.
LogiGun is a mostly-puzzle physics platformer, with a sensible difficulty level.
Stealth Inc 2 is a puzzle platformer I suppose, involving clones.
Nethack and Slash