aBridge supports speech synthesis, allowing you to choose to listen to the bids and chat conversation rather than simply gazing at the screen waiting for someone to play. aBridge also has some rudimentary bots, for when other players aren't online, but their AI is pretty pathetic, and they are in need of a complete rewrite.
Back Alley Bridge
Back Alley Bridge is a simple card game with trump. It requires GTK+ 3 and sox.
Bridge Calculator solves problems in the Bridge card game. It solves the double dummy problem, has both graphical and console-based user interfaces, and imports deals from files generated by the KoPS program.
PyBridge is software that lets you play the card game of (contract) bridge with human players over the Internet or a local network. It has support for bidding, trick playing and duplicate scoring.
(commercial) Xcontractbridge features random deal, conventions including Stayman, Baron, Jacoby, ACOL bidding system, with a random deal engine.