Firefox because of the addons.
For me it's Firefox, running 3.6.13 (newest).
If you want to test out Firefox, Opera, and Chrome without really installing it, I would download and install Sandboxie. It runs them in a sandbox and won't clutter up your registry.
I like Firefox because of the Addons. My main ones are Tab Mix Plus, NoScript, CookieSafe, AdBlock Plus, DownThemAll!, Highlighter, SearchWP, IETab 2, and Scrapbook. You can also run many different profiles in Firefox, so can use different users for different bookmarks and Addons to see what works best.
I love Tab Mix Plus, it saves the last 2 sessions (or crashed session, if applicable) or you can save any session permanently for later use. I usually have 15-20 windows with 55-75 tabs that I always like starting up. There is no way I can read everything that I open up, most of the time I read a little bit here and there and check back 1-5 days later to see if any new updates. Some pages I always like to come up. You can also set the tab your on to a different color, bold it so it stands out more and you know what tab your on if you go to another program or come back later.
Highlighter Addon is nice, you can highlight 5 different colors within a page. For instance I use it for Excite TV and use yellow for ones I'm recording, green ones for ones I might want to watch in real time and blue ones for might watch on OnDemand.
The Scrapbook Addon is nice because you can save the whole page and take notes on it and save it to your hard drive. It also can be used with the Highlighter Addon, but Scrapbook also has it's own different color highlighting and the option to save a page and you can take notes on it and save it on your hard drive for research.
The SearchWP Addon is very nice, if you want to search for multiple words you can. For instance want to search for multiple terms that are the same but different spellings: win7, "win 7" "win7 updates" all of these can show up in different colors and you can click them and they go to the next and next. Very helpful.
DownThemAll! is very nice for downloading numerous podcasts on the same web page, saves a lot of time.
NoScript, AdBlock Plus and CookieSafe, you can almost go to any website and not get malware or a virus, especially if you have it running in Sandboxie. But with Sandboxie you really don't need these safe browsing Addons anyways.
I use IETab 2 because some websites are too lazy to write good code and you have to use IE. But you still use your Firefox bookmarks with it and RoboForm still works with IETab 2.
I've tried them all recently and I'll say that Chrome was fast. But with my 3 safe browsing Addons, there is no way it could be faster than Chrome. Chrome had a NoScript option workaround IIRC a few months ago but I didn't like it at all.
I also tried Opera in Sandboxie and I liked it, but really no Addons to speak of. IE7 and IE8 I don't like at all, I hate many things about it and especially how they handle bookmarks. Firefox's bookmark manager is very, very nice to use.
I would say install Firefox and look into some Addons. Others I use are CNExtend for Cyber Nations and Mouseless Browsing with Dragon Naturally Speaking. There are so many for so many occasions it can get confusing, but over time you will find that you don't need some at all and others will be very handy. Firefox also is easy for making TOR work. A must is having NoScript and/or TorButton because without fully stopping Java, Silverlight and Flash, being anonymous is impossible.
Again I would install all 3 of the others in Sandboxie and pick one works best for you. I personally installed another separate Firefox with Sandboxie for TOR use and another profile to test out new Addons. Firefox can also be used on a flash drive as a
portable app and you can save all the settings on your desktop or laptop just like you were there. Case in point I copied my profile settings (all Addons, extensions and bookmarks), so when I went to my cousins house and used his PC, all my windows and tabs I had at home were exactly the same, like I never left my PC.
For me it's:
1. Firefox
2. Opera (was just chosen in Jan '11 by Sony for their TV's and BluRay players with internet access)
3. Chrome
4. IE8