Bask in the glow of over-bright phosphors that flash on and slowly fade away. Customize the screen's curvature, colors, and transparency. Slow the bit-rate to a crawl.
Watch the strange dance of beam desyncs and shifting colors. Turn up the noise, jitter, and flicker to add a realistic warmth.
Disregard thirty years of GUI advancement by immersing yourself in full-screen mode. Impress curious onlookers at internet cafes.
Getting a lot of hits on this one... For those of you tuning in late, or who don't click my "previously" links, back in 2006 there was an earlier program of similar concept called "GLTerminal". This new "Cathode" program works a lot better, though.
For those of you on Linux (or using X11 on a Mac), you can accomplish a very similar thing by using the "apple2" module of my xscreensaver package, as detailed here (and also here and here). The underlying display module shared by the apple2, pong, m6502, and xanalogtv screen savers is actually simulating the hardware of an old CRT, rather than just doing an effect that kinda-sorta looks like it. Reading all of the comments in hacks/analogtv.c is well worth your time.
Update 2, 2012: Hey, as of release 5.19 in late 2011, the MacOS release of XScreenSaver includes stand-alone application versions of the Apple2 and Phosphor screen savers that are pre-configured to work as terminal emulators. Check them out.