Several things:
the 2nd gen has a "contour design" that fits perfectley into the palm of your hand.
the 2nd gen has a bigger screen
the 2nd gen is thinner
the 2nd gen has much better graphics
the 2nd gen has 17 apps when u buy it, compared to the 1st gen's 11
the 2nd gen has more compatible applications
the 2nd gen has "coverflow", a device that allows u to turn the ipod sideways while listening to music and it will show all of your albums in 3-D and, with the flick of ur finger, it goes through the albums. when u see an album u want to listen to simply touch it and select a song from the list. U probably have no idea wat im talkin bout but its the absolout most amazing thing you'll ever see (if you search for ipod touch guided tour it will show the coverflow feature) The 1st gen soes not have this
the 1st gen is cheaper
if you want my advice, hands down no doubt about it get the 2nd gen, it is totally worth it.
One last thing, you've gotta know how many gb you'd use, because the 1st gen touch 16gb costs the same as the 2nd gen 8gb. If you've never had an mp3 before I'll tell you this: 8gb goes way, way, way, way, slower than you'd expect. I have 43 apps and 160 songs and I still have 5.93 gb's left.