Disable JOIN and PART Messages

mIRC

Tools -> Options -> pick "IRC". Click the "Events..." button. Change the "joins", "parts", "quits", and "nicks" to your desired settings: "In Status" or "Hide" are good options.

XChat

To hide parts and joins on all channels, you can use /set irc_conf_mode 1.

To hide parts and joins for a specific channel, you can right click the channel in your channel tree/tab, click Settings, then click Hide Join/Part Messages

Snak

Snak -> Preferences -> Channel, and uncheck "Parts" and "Joins".

Irssi

/ignore -channels #channel * JOINS PARTS QUITS NICKS

BitchX/EPIC

/ignore #channel * CRAP