Fritz - A German chess program originally developed for Chessbase by Frans Morsch based on his Quest program, ported to DOS, and then Windows by Mathias Feist.
GNU Chess - A free software chess engine which plays a full game of chess against a human being or other computer program. The goal of GNU Chess is to serve as a basis for research. It has been used in numerous research contexts.
Leela Chess Zero - A free, open-source, and neural network-based chess engine and distributed computing project.
Chess computers
Deep Blue - Chess-playing computer developed by IBM. It is known for being the first computer chess-playing system to win both a chess game and a chess match against a reigning world champion under regular time controls. (quick update 2023-2-4: 403 Forbidden)
Belle - Chess computer developed by Joe Condon (hardware) and Ken Thompson (software) at Bell Labs. In 1983, it was the first machine to achieve master-level play, with a USCF rating of 2250.
AlphaZero - AlphaZero is a computer program developed by artificial intelligence research company DeepMind to master the games of chess, shogi and go. Chessprogramming wiki on AlphaZero.
Lila - A free online chess game server focused on realtime gameplay and ease of use.
Chess Alpha Zero - Chess reinforcement learning by AlphaGo Zero methods.
python-chess - A chess library for Python, with move generation and validation, PGN parsing and writing, Polyglot opening book reading, Gaviota tablebase probing, Syzygy tablebase probing, and UCI/XBoard engine communication.
Game Server - Distributed Java game server, including cluster management server, gateway server, hall server, game logic server, background monitoring server and a running web version of fishing. State machine, behavior tree, A* pathfinding, navigation mesh and other AI tools.
Tensorflow_chessbot - Predict chessboard FEN layouts from images using TensorFlow.
Command Line Chess - A Python program to play chess against an AI in the terminal.
Websites
Chess online for instance.
chess24.com - Free live chess with humans or computers, watch games, chat and join tournaments.
chess.com - The chess community with +30 million members around the world.
lichess.org - Lichess is a free and open-source Internet chess server run by a non-profit organization of the same name.