I'd never thought about the character limit on domain names — but apparently, they cut off at 255. I found a handy Microsoft blog that goes into a bit more depth about it, citing RFC 1035 section 2.3.4.
Someone who clearly knows more about this than me already had the clever idea to max it out by registering. http://a.b.c.d.e.f.g.h.i.j.k.l.m.n.oo.pp.qqq.rrrr.ssssss.tttttttt.uuuuuuuuuuu.vvvvvvvvvvvvvvv.wwwwwwwwwwwwwwwwwwwwww.xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx.yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy.zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz. This fun little experiment has some intrinsic added value, too, as explained on the site:
The domain is created to reach the maximum number of allowed characters (255 (really 253)) with an exponential curve in the length of the letters as you proceed through the alphabet. The formula used is "1 + 62 * (10/7)^(x-26)". To help illustrate this curve, reference the distribution on this spreadsheet. It's colorful because I like colors and wanted to do a progressive "rainbow" animation in CSS3.
Who.is couldn't give me any information on the name of the owner/creator of this site. But I commend them nonetheless.
Image: Kulandru mor / Wikimedia Commons (CC 1.0)