Ah, this has been one of my obsessions over the past several years while flying United. I've been keeping track of the aircraft I've flown by their "N" registration numbers, as well as the nose number as referred to by UA.
Incidently, the 2nd digit on the nose number is actually the differentiator for interrior configurations. For example, there have been several different nose numbers for the 744, 84xx, 80xx, and 81xx. As far as I can tell, they have all been standardized to 81xx now.
Here's a run down of the type and associated nose numbers (some may be obsolete):
733 - 99xx, 98xx, 13xx
735 - 16xx, 15xx
744 - 81xx
752 - 54xx, 56xx, 57xx (PS)
763 - 67xx
772 - 26xx, 29xx
319 - 40xx
320 - 46xx, 47xx, 49xx (Ted)