Seamonkey - Uses less resources but shares a lot of code with Firefox, so it has a familiar feel
Epiphany - Very light weight, however requires a lot of GNOME dependencies
Midori - Very very light weight, but very beta right now
I actually recommend Seamonkey over the three listed above. Sure everyone has their favorite, but Seamonkey also benefits from the extensive mozilla plugin system. The 2.0 version is about to go beta, and runs very well in its alpha state. I've been using the nightly builds for a while now. I originally installed it on the infamous Compaq refrenced in this article, but I loved it so much, its now my browser of choice, even on my dual core 2 gig machines. Its very snappy.
Just a few thoughts on a difficult subject. If you have the resources to spare, Firefox might be the way to go, but there are alternatives for the adventurous in all of us.