All of the browsers archived here can be run on modern machines -- some directly, some via emulation in the browser, and a few only on dedicated emulators running outside the browser.
Run directly
LineMode compiles easily on modern systems. You can test out LineMode 0.11 and 3.1 by connecting to browsers.flanigan.us via telnet with username wwwlinemode_0.11 or wwwlinemode_3.1, or by visiting the archive's LineMode page.
Cello can be emulated using js-dosbox on the archive's Cello page in Windows 3.1. It will also run in Windows 95.
Emulate
The following browsers can currently only be run on real vintage hardware or in dedicated emulators outside the browser:
MacWWW/SAMBA runs on Macintosh System 6 through MacOS 9, but requires a working network connection. BasiliskII and SheepSaver work well for this purpose. (See also Edward Mendelson's pre-built wrappers.)
Erwise can be built with GCC 4 on Ubuntu 9.10, which is easily emulated or virtualized, using patched source code available here.
MidasWWW 1.0 compiles and runs on Solaris 2.6. A partially-working patched version also compiles on Debian Stretch and will run via Valgrind.