Benzo is a pseudo-AI bot written in Python. In addition to providing humourous chatter, it performs basic IRC channel maintenance functions. It is written in a modular fashion, so adding commands and functionality is trivially easy. Benzo's 'brain' is a Markov Chain, which uses probabilites gathered in the input text to produce pseudo-random output.
TilkIRClog is a program designed for logging chats on IRC channels, written in Python. It doesn't intend to be an IRC client, so it's fully automated and has many useful features. For example, it can automatically send logs via e-mail, and even compress them. It can also be restarted from a cron job after termination.
Supybot is a clearly-written Python IRC framework and bot, intended to be both easily extensible and very flexible. Several modules are included by default. Numerous plugins are already written, including Google, Factoids, RSS, Quotes, and Relay. Plugins and their commands achieve greater utility via command nesting, something that no other IRC bot does. The user database is based on "capabilities" rather than obscure flags or arbitrary numeric "userlevels", giving the bot flexibility and fine-grained control (think ACLs vs. standard *nix permissions). Developing your own additions to the bot is simple with the base classes provided; writing a new command for the bot is as simple as writing a function. Unlike many other IRC frameworks, this simplicity is achieved at no cost to generality, which lets new programmers and old programmers alike feel at home in the framework.
Pynfo is a combination IRC info, search, and network relay bot. It supports basic fact definition (with persistence between runs) and searching of Google and Dict.org. In the network relay mode it "bridges" channels on different networks by passing messages between them. It also has a plugin interface, allowing users to easily define new commands.