mIRC
mIRC is the most popular piece of software used to access IRC. IRC, which stands for Internet Relay Chat, is even older than the World Wide Web.
IRC contains many networks with many channels in each of them. For example, connecting to the network irc.LCIRC.net and joining the channel #albinoblacksheep will bring you to a chatroom full of visitors from this site. They can chat, private message and direct connect to send files. Check out the Chat directory of this site for instructions on how to join us.
I must point out that mIRC is not the only IRC client. There are many other programs, including IRC programs built into browsers like Mozilla Suite and instant messengers like Trillian.
mIRC is losing some popularity, at least with me, since the new versions often popup messages to register the program when its not actually necessary to do so.
I also might have something against its author. Nevertheless, for a $14 well-secure and supported program, and free full working demo of the same, mIRC is ideal for accessing the old part of the Internet, IRC.