Breeezy is a version of the Safepup variant of Puppy Linux, customized for the Eee. It is very fast, installs easily to an SD card, works well in a dual-boot system with XP, and it is easy to install additional software on it. It comes with Firefox.
Raffy Mananghaya is the driving force behind Breeezy and he maintains comprehensive information on it here.
Why would someone want to use Breeezy? In my case, I lived with the stock Xandros OS for a while and found that it didn't fully meet my needs. I installed XP so I could use some software that I didn't want to take the time to learn to run under Xandros. Yet, I wanted to play with Linux and to have a fast booting system that would not have the overhead of virus- and spyware-checking software. For me, Breeezy is a good solution. I keep it on an SD card that is always loaded in my Eee. When I want XP I boot into that, and when I want Breeezy, I use that.
I encourage you to give Breeezy a try. Raffy is very helpful and is honing it so it is an even better fit for the Eee.