Firefox used to be king, with new features (like tabbed browsing) which we now take for granted. It also used to be a lot faster than IE. However, it also gets bloated faster than most other browsers, as soon as you start adding plugins. For web development it's probably still the best with great debugging tools.
IE is still carrying a bad reputation from IE5-8 which were, frankly, woeful... slow, buggy and with security concerns by the bucketload. To be fair to it, the newer versions (10/11) are much improved, but I still don't trust the OS integration and I don't go back to a bad product just because it's pulled itself up to average.
Safari is great if you use iOS or OSX on other machines. It works very much like chrome to me - simple tabbed browsing without much clutter. If you don't use OSX/iOS however, stick with Chrome/Firefox - it's not worth being pestered to install Quicktime constantly...
Chrome is the current king for most: it's usually fairly fast and lightweight and does the web browsing bit without a load of messing about you don't need. I switched as my primary browser when it first came out and haven't looked back since.
Waterfox is a souped-up version of Firefox: I've not tried it, but most of what I've seen suggests that it's basically an optimised version of Firefox.
Then there are the niche ones like Opera - which I used to love but found it was trying to be too clever. Like Firefox it came up with a lot of new stuff, but the main browsers have mostly closed onto the basic Chrome design.
Overall, it's usually down to preference nowadays - there's no real significant differences between them. Chrome is probably the best choice for most who just want browsing. Safari if you use OSX on another machine, Waterfox/Firefox/Opera I have installed for web development or in case there's an issue with chrome... or if you don't like google. IE... I still don't see why you'd actively choose to use it, Microsoft made bad browsers for too long for people to switch back just because they're okay nowadays.