Games

Emulation

Vimm's Lair
Emulation Wiki Overview of all existing emulators, often with information on obtaining bios files
PC98 Emulation FAQ
Obtaining ROMs Guide by Imakuni Despite being a Tumblr post this is actively updated and passes muster
Myrient
NoPaystation
Darthsternie's Firmware and Exploits Archive firmware/bios archive

Puzzle Games

Dragonsweeper Minesweeper variant
Daily Akari
Puzzmallow
Seattle Times Puzzles Republishes things from a few other sources, allowing you to play them for free
Mamono Sweeper Minesweeper Variant
A Sweeper of Mines minesweeper variant
Bloquecitos Physics game ala Suika Game, but featuring chunks of decorative ceramic tile
Jigsaw Planet Allows for custom puzzles, including private ones
Nonograms.org Has both color and black and white
Enclose Horse Maximize the space of the horse's pasture with a limited number of walls
The Atlantic Puzzles
Trails
Clues by Sam
Gisnep
Puzzmo