That depends how you define anonymous.
You can specify a nickname and identd that are nothing related to you, but your IP / Host mask will be tracable to you.
Vhosts
A normal ' /whois ' on a user, may return the following:
MedNez!med@111.d3.bigpond.net.au
In the format of Nickname!Ident@hostmask
A vhost (virtualhost), transforms that into the following:
MedNez!med@whatever.you.want.com
However, you have to buy virtualhosts, and they can still be traced back if one has the right knowledge and technology to do so.
Invisible Mode
Most IRC networks have the +i option, which sets you as invisible on the Network, but that doesn't really give you anonymity.
Network Protection
Some networks, such as Austnet (the network #hsc is on), provide an automatic masking system for their users.
So instead of MedNez!med@111.d3.bigpond.net.au, it appears as MedNez!med@vw22350.bigpond.net.au , or a similar vwXXXXX code, to hide your actual address.
This however, too, can be bypassable unfortunately.
Proxies
If you are behind a proxy, you might have 255 computers on your network, and if one of them connects to IRC, depending on the setup you may all have the same IP. This does, in a way, make you anonymous to the outside because it could be one of two hundred and fifty five people, however that's not really a help since you can be traced internally if you're doing the wrong thing.
Programs, Packet blockers
Programs to capture information request packets, alter them, and send them back can be obtained, but
1) Don't always work
2) Can be malicious and not worth the risk
In short
There is no anonymity on the Internet. You can always be traced, no matter how high the skill level (assuming you don't work for some Government Intelligence Organisation ;P), and I can't really think of any reason you'd want to have absolute anonymity on IRC unless conducting dealings that may or may not be appropriate or morally correct.
I hope this has given a bit of help - you can't become _absolutely_ anonymous, but you can make it more and more difficult for someone to trace you.
Regards,
MedNez