My favourite by far is
Quasseldroid. There is a beta in the google store. It's a port of the Quassel IRC distributed IRC client. It's similar in concept to screen/tmux & irssi. You run a Quassel server on a box somewhere (the desktop version can run standalone as well) and then connect to it with a client - quasseldroid, quassel2go, or the desktop (linux/win/mac) client. The only caveat with Quassel is that there is no DCC support.
Since I mentioned irssi, I feel obligated to mention
Irssi Connect Bot It's a modified SSH client intended to make irssi usable on a touch screen. I strongly prefer a GUI on my phone, but this is a pretty sweet setup as well.