Yes, there is a record for the most miles covered in 24 hours. It is usually set on a 24-hour challenge such as these:

http://www.n24hc.org/event.html (pop over to the 2005 results and you'll see that the guy who did the most miles covered 470 miles in 24 hours)

http://www.big-dogs.org/umw/UMCA24/UC24Main.aspx (check the roster and you'll see I'm signed up!)

http://www.tt24tt.com/

http://www.mersey24hour.co.uk/index.html


As for sleep ... you don't need to sleep on a 24-hour event!!


If you are interested in other long distance events check out Randonneuring:
http://www.randonneurs.bc.ca/links/links.html
http://www.rusa.org/

And here's a couple generally useful sites for information about events, training, nutrition and equipment for long distance riding:
http://www.ultracycling.com/
http://www.bikecenturies.com/