I know this might sound archaic to most of you, but I use lynx as my main browser, and it doesn't support Javascript (and thus AJAX). I use Lynx because I prefer it to the bloated graphical browsers. It runs in a terminal with the same nice fonts I use when coding (in Vim, another "archaic" tool, I guess). It can run under a GNU screen session. It supports some level of scripting and automation, using simple Perl or shell scripts (and works exquisitely well with the "surfraw" search tools). It can be used exclusively from the keyboard, which is a big plus for me, especially when using a laptop that doesn't have a proper pointing device (not that I much enjoy reaching for the rodent in the first place). It let me bypass all the ads and junk on the web these days and focus on the content. It's also fairly secure, especially when you consider I'm using the version that ships with OpenBSD.
I have used this web browser since 1995 (an age when many gopher sites were still active), and feel that it still delivers a web experience that's above and beyond what the others do (the "links" family comes close though). It would be a great pity if perlmonks changed their site in such a way as to make it unusable for anything but the graphical, mouse-intensive, java(script) ladden heavy browsers that are common these days.
Some of the concerns I bring up may also apply to WAP devices, though I can't be certain about this since I don't use those myself.