another BIG vote for firefox here! It is the *****! Loads of well though out plug ins and its light-wieght, fast, SAFE, intuitive, nicely designed, customisable, doesnt need to be installed for anything else to be installed... the list goes on and on and on.
Did i mention safe? Ive never contracted a virus, a malicious active control with firefox. My spyware software is now all but redundant (cleans up cookies only now). It tells you when you need to update it, and its fast and easy, no restart needed.
As for imcompatibilities with some sites, these tend to be very few and far between and not properly designed in the first place. If you really need to, you can always open that site in IE (theres even a plug in which will do this automatically for you).
Weaknesses?? not likely...
Whats not to like about it?