Webchats allowing access to IRCnet via a web-browser:
http://www.mibbit.com/ * Includes IRCnet in their dropdown menu
http://irc.tu-ilmenau.de/web-irc/ * Germany only (standard CGI:IRC or a Javabased one)
http://www.irccloud.com/ * Includes IRCnet in their dropdown menu (requires free registration)
If you want a dedicated program with more features, see our IRC clients page.