One of the forums ran a Game Chef design competition back in March 2009 with some odd constraints, including "completely random characters". My entry was Resist the Atom!, a mixed resistance fighter/supers game where the supers are the enemy. I included a character sheet that you rolled dice on to randomly assign scores to ten attributes. Here's an excerpt from the character creation section:
The first step is to create some characters. Take a look at the character sheet: it has an outline of a human form and four grey lines that divide the sheet into various regions. There are boxes at the top for the character's name and player's name, and also ten boxes to write stats in. Six of the stat boxes are in pairs, with a single label for both stats in the pair. There's space for writing a short character description under the names, skills and backgrounds on the left, and important items owned on the right.Head Arms, and Legs represent pairs of stats covering sensing, acting, and moving. Each has a speed and a power. Body is a single stat (essentially, hit points/Con,) and there were three other stats, Age, Resources, and Secrecy (secret resources.) All characters start with Speed stats of 4, Power, Body, and Resources stats of 3, and Secrecy of 1; Age is calculated from skills or defaults to 25. The gimmick was that you rolled dice on the sheet and assigned each die result to the stat it lands closes to, or two or three stats if a die lands on a line. Everything else stys at the default. You also roll on the sheet for resources, equipment, special backgrounds, and abilities (using the names of the stats to determine what you have for each.)
The arrangement isn't just artistic, it's practical. You can roll dice directly on the sheet to randomly determine hit location in the four basic areas: head, arms, body, and legs. You can do the same for non-human objects and interpret the body parts by analogy, or if you're stumped for ideas you can use the regions of the character sheet metaphorically. This is also the key to random character generation: you roll several dice directly on the character sheet and determine which stats to change based on where the dice land. Dice that land roughly mid-way between two or three stats affect all of them, so even rolling just one die can produce a lot of variability.
At some point, I will probably use this as a template for random haracter generation. I already tried a more abstract approach (you can use the right-hand column on the Quickie Dice Tool, for example.) But I like the way the character image doubles as a hit location chart.