I'm thinking that in order to make such a list much would depend on ones own definition of 'cheap' - intended use, how much you were prepared to compromise and/or upgrade/repair...the variables are endless...
For Instance - my own pride and joy is an original red Triban 3 £299.95 brand new and a pukka out of the box road-bike..........,
www.cyclechat.net/threads/beginners-joy-a-pic-of-my-new-ish-pride-and-joy.115948........ since marginally upgraded and rides more than well enough FOR ME...but other roadies still snigger at it!.....but most agree there has never been a bargain cheapie like it before or since.
For a little over 100 smackers i rebuilt a totally unrideable shagged out shed-bike into a tasty little roadster using cheap internet parts.....which satisfies MY USE for it.......
www.cyclechat.net/threads/shed-rescue-bike-rides-again.149757
But all depends on that definition of 'cheap'. Impossible to quantify.
Beauty...useability....cheapness ...all in the eye of the beholder.
However..Tom Allen (round the world cyclist, adventurer, blogger/filmaker) experimentally built a World-Tour-Ready bike (by scavenging/blagging and scouring for 2nd hand/junked parts) AND sourced all the equipment to use as such for less than £28.00! (to see if it could be done!!) It Could.
Read about it by googling his blog? (I'll try and link when I have a mo)