I think I can add quite a bit to this discussion; I just hope I don't piss anyone off.
If you're in the console, Lynx Still Rox! The main problem is lack of scripting, since so many sites require you to have it these days. There are still some older web sites that are more or less Lynxified still, though. One BIG recent problem: apparently NVIDIA is refusing Lynx connections--this is a bitch when you're trying to download the blob! So far, no response from their webmaster...
Now, for regular (graphical/scripted) browsing, I prefer the Firefox and/or Seamonkey (I'm assuming other Gecko browsers would work, too) because of the configurability, and especially the plugins; this isn't anything anyone else hasn't said before. One problem: recent versions 17 and 18 are dramatically slower than the previous 15 and 16. This not only appears to be fixed in 19a2 (alpha aka Aurora), but it appears to be the fastest Firefox I've used in years! Caveat: it's on the win-xp machine at work, I have yet to install it on my laptop running Slackware64-14 (not current at the moment).
There is a catch to Gecko, though: it's single-threaded. If you're using multi-core Atom, Fusion, or other slow-per-core arch, you'll significantly-to-insanely faster response from one of the other browsers: everyone is multi-threaded except Gecko. On our guest lobby machine here at our motel (which is a 2011 Black Friday special dual-core AMD E300 running win-7), Opera and Chrome are far faster than Firefox; the difference is there, but less pronounced (except on FF 17/18), on this E8400 Core-2 Duo machine; and I have never run Opera or Chrome on my dual-core AMD Turion X2 laptop, so I can't compare there except that FF can get really unresponsive when the cores are still stuck at their lowest clock of 800 MHz.
I mentioned I've tried Opera and Chrome, both on the lobby machine. Both are fast, but both are far more difficult to configure the way I like them. I never liked Opera 12's layout, and I ended up HAVING to pull it because Delta Airlines did a web site re-design that broke a lot of crap, including Opera compatibility, as it turns out. I like Chrome's layout a lot better, but don't like that there is no way to force Incognito Mode (private browsing) on startup (come to think of it, I don't remember figuring out how to do it on Opera, either, but with Chrome, Google seems to go out of their way to keep you from turning it on permanently). Thus I stick with Firefox where I can. I just wish Mozilla would get their head out of their ass and realize the entire world is going multi-core and they're getting left behind by not getting serious about re-writing Gecko to be multi-threaded.
I have always had the worst luck with Konquerer: it just loves to crash for me. Then again, many KDE apps crash on my machine, mostly the more obscure ones; ones I actually need, like K3B, seem to work ok most of the time.
I have not tried Dillo, but based on all the positive reviews I keep reading about it (in other threads besides just this one), it seems I really need to check it out.
I never really like Links that much, though I don't think I ever really used it to its full potential (graphics mode and all).
I hope this helps,