I use Chrome Beta on my Galaxy Nexus, and mostly use Chrome on my desktop. A great app is Chrome to Phone, which automatically syncs open tabs on my desktop with my phone. Or I can choose which tabs to send to my phone and then close my desktop browser completely and have those tabs ready when I open Chrome on my Nexus. Very cool. Plus all my bookmarks are automatically synced to my devices as welll
I tried Dolhpin but had a lot of trouble with it, I think I have two favorites. One is Firefox and the other would have to be Opera. Opera is stable and never crashes on me.