http://thecolourclock.co.uk/ - Takes the hour, minute, and second, divides them by 23, 59, and 59 (respectively), multiplies them by 255, and changes the red, green, and blue values (respectively) of the background color to those numbers. The effect can be pretty relaxing! Currently it is blue in my time zone, since it's just after midnight.
http://www.ruinsofmorning.net/flash/hexclock.php - Hexadecimal clock with 16 hours in a day, 256 minutes in an hour, and 16 seconds in a minute. Currently reads 0:32.D.
http://www.alphabetclock.com/ - Uses letters instead of numbers, with A=0, B=1, ..., Z=25. 26 seconds in a minute, 26 minutes in an hour, 26 hours in a day, 26 days in a month, 26 months in a year, 26 years in a century, and 26 centuries in a millenium. Since it's synchronized to UTC, it currently reads FJSYD:STM even though it's just after midnight right now. (FJSYD: is the date and :STM is the time; the first few letters of the date can be omitted depending on how specific you want to be, like how you might abbreviate 2011 to '11, say "October 24" with no year, or say "the 24th" with no month or year) Also includes a time and date converter.
Interesting finding - :ENYA is 11:11:11 AM in my time zone...
http://www.purplemassgroup.com/upload/wtf/index.html - Custom version of the previous clock that shows two more digits of the time and includes a calendar.