I use Firefox and have been doing so since before the name change from Firebird (which occurred early 2004) and whilst I have tried other browsers I find a lot of them lacking.
There's Lynx, Links and ELinks but they are text only (well elinks does support a vesa graphics mode I believe but I haven't tried that) and can be a little difficult to use and navigate. There's also dillo but it's SSL support is alpha only at the moment, it doesn't support frames and it's support for image formats seems a little limited.
I find Firefox somewhat better than these although out of the box it's got some annoying limitations - luckily it has extensions. In the past I had to add 20 odd extensions just to make Firefox "almost un-annoying" to me but thanks to Mozilla adding these features in Firefox over time, I've got my extensions list down to a mere 9 which I will detail below (roughly in inverse order of importance, just for fun).
- User Agent Switcher (https://addons.mozilla.org/)
This extension allows you to change your User Agent, also allowing you to switch between user-defined User Agent strings. While a lot of people use this to visit websites that say "I'm sorry, you need Internet Explorer to view this" when it would render fine in Firefox, I use it just to set my User Agent to something more generic (namely "Mozilla/5.0 (X11; U; Linux i686; en-US; rv:22.214.171.124) Gecko/2008123017 (A browser built upon the highly renowned web standards compliant and secure Gecko rendering engine that is the heart of several open source web browsers, including Camino, Epiphany, Firefox, K-Meleon, Mozilla, Netscape, SeaMonkey and XULRunner)", an idea I got from Mozilla Firefox Bug 334967 (https://bugzilla.mozilla.org/)). In fact if a website says "You need Internet Explorer", I just take my business elsewhere.
- Add Bookmark Here² (https://addons.mozilla.org/)
I realise while writing this, that I don't actually use this extension anymore but only because it doesn't really work with another extension I use that I cherish more. Add Bookmark Here² adds a menu item under each subdirectory in your Bookmarks called "Add Bookmark Here". This is a lot more intuitive and natural feeling than using Firefox's Add Bookmark dialog to navigate to where you want to place your Bookmark.
- Duplicate Tab (https://addons.mozilla.org/)
This little beauty is essential when dealing with annoying pages that require you to click something and won't accept it when you open them in a new tab/window etc. It simply allows you to duplicate any given tab to another tab or window, including it's history.
- Image Zoom (https://addons.mozilla.org/)
This extension allows you to right-click any image and zoom it to any size. This is a great little extension if you need to get a closer look at an image. As of Firefox 3 "zooming" the page no longer zooms just the text but also the images making this extension less necessary but I still find it better to turn that feature off and reserve their "zooming" to text only and leave the image zooming to this little extension.
- Stop Autoplay (https://addons.mozilla.org/)
Stop Autoplay allows you to disable autostarting of embedded media (or exclude it altogether) as well as blocking Flash (though I don't use that feature (see below)). Quick, simple, NECESSARY for those dodgy GeoCities or MySpace websites that spew audio at you obnoxiously.
- Nuke Anything Enhanced (https://addons.mozilla.org/)
Ever had a website that brought up an annoying "popup" within the page, blocking the content and not allowing you to read it until you clicked something? Maybe you want to print the page without all the unnecessary images (Note I haven't actually tested this extension for this purpose but I THINK it'd work)? Well, this extension will allow you to right click ANYTHING (yep even a table cell, paragraph, image, frame, div etc) and select "Remove this object". Until you try this, you have no idea how satisfying it is!
- Adblock Plus (https://addons.mozilla.org/)
This extension will block ads from websites so that you don't have them in your face whilst trying to read the content. You can subscribe to ad list databases and even add your own manually or automatically (right-click any ad and say "AdBlock this"). I am actually torn with this one as I realise some sites rely on their ad revenue to fund their hosting etc. I would advise anyone who feels this way to still have this installed (but not subscribed to any database) and simply use it for the really obnoxious ads that insist on flashing in your face.
- Flashblock (https://addons.mozilla.org/)
The web today is unusable without this extension. This extension is more advanced than Stop Autoplay's Flash blocking capabilities because it still reports to the website that you can handle Flash but it won't actually load the Flash unless you click a cute little play button. Stop Autoplay is aware of this extension and won't fight for Flash control if it sees it (so they play nice together).
- Vimperator (http://vimperator.org/)
This one changed my life. It's the best extension EVER. It is designed to allow you to operate Firefox as you would VIM, including many of the same shortcuts and commands. The good thing is you can have it installed and still use Firefox normally and just take advantage of the features you like. It has a most excellent keyboard link navigating system where you press 'F' and start typing the text of a link. As you do so, the list of available will reduce until such time as there is only one left at which time, it is "clicked". While this is happening however, the links matching the text you've typed will be highlighted and numbered so you can optionally type a number at any time to follow that specific link. Features like this make keyboard navigation quick and painless. It has many other features worth looking into too - check out their website for more details. In short though, if you use VIM (and Firefox) you NEEEEEEEEED this.
Well, that's it. My list of required extensions to make Firefox really usable and an almost painless experience.