(1000 = First PSP series, 2000 = Second and 3000 = New PSP Series)

PSP-1000 vs PSP-2000
*2000 is 19% thinner
*2000 is 33% lighter
(These can be pros or cons, depends how you feel about it, for me I prefer the 1000 as it feels more sturdy)
*2000 also has more RAM, 64mb compared to the 1000's 32mb, this allows the 2000 to use Go messenger and skype as it has more RAM, haven't tried these so im not sure how well they work.
*2000 also has a slightly more brighter screen, supports USB charging, redesigned so you can connect it to a TV and play, (only if the TV supports progressive scan)

PSP-2000 vs PSP-3000
Like the 2000 but with some extras, Dont know too much on the 3000 but here's some stuff I found on it:
*Improved LCD screen (not in overall brightness but the colours, eg Reds are now more red, Google "PSP-3000 screen head-to-head with the PSP-2000" to see what I mean)
*Expanded Video Out, like the 2000 but improved I guess, not sure what's improved though
*Built in microphone