I'm not OP, but I think it has got to be the white MacBook with the Intel X3100 graphics. Out of interest, I bought my wife the first aluminium MacBook that would have been released on the same day as his laptop, and that does support Mavericks (because it has Nvidia 9400M graphics, which the next year's white MacBook then also got).
It's a shame those old white Macs (including white C2D iMacs) don't support Mavericks, because they are 64-bit capable and generally still reasonable machines. But support has to stop somewhere, I guess, and I wouldn't like to be the person writing the 64-bit firmware and drivers for those machines, 6 years later. Also, most of them have got dodgy GPUs thanks to a combination of poor Nvidia parts and all-in-one/ultra-slim designs that got clogged up with dust.
FWIW, if you're programming for the AppStore (i.e, using these as a professional tool), 5 years of life out of a laptop is actually pretty good (IMVHO). I get at least three years of use out of my Macs (currently on a Nov 2010 MBA) before I start thinking about upgrading/replacing, but that's still going strong.
Adrian was almost correct: I have a Black MacBook 3,1 (not white!), which has the X3100 GPU and a 64-bit 2.2Ghz Core 2 Duo. I've upgraded it to 6GB RAM, 1TB Drive, brand new battery, and even considered swapping out the CD drive to add an SSD. It's more than a match for a brand new MacBook Air.
I installed Mountain Lion today on it by using MLPostFactor, so my own crisis is resolved... but it also shows that the machine is completely capable of running Mountain Lion. The only thing stopping it is Apple (and a lack of 64-bit X3100 drivers).
