If you want a fast, stable, and feature-thin text browser, use Links-0.99. Main drawbacks include: No HTTP-auth support and no persistent cookies (i.e. they die when all instances of Links are closed).
If you want additional features, including HTTP-auth, persistent cookies, and on-the-fly compression, try ELinks. (Note: links-0.9x and ELinks versions > 0.3 do not share executable name or configuration files so you can safely run these on the same machine.)
If you want the option of graphics mode, use Links2 or Hacked Links. Be aware that some people have reported the latter as hard to configure/compile. You cannot run either of these with Links-0.9x on the same system without hacking the compile-time configuration.