2E And 3E used the priorities (ABCDE) system. I don't know about 1E or 4E (haven't played them). Mechwarrior (another FASA) game used a "you get ten points" 0,1,2,3,4 system for character generation.
I liked shadowrun, and it stands out for me because it was the first non-D&D game I ever played, and one of the first times I was the player, not the GM. Me and my friends inherited a bunch of SR books from my friend's brother, who had had enough of the game (moving on to Vampire, I think, although he later became a BIRTHRIGHT freak).
Most of our games were violent bloodbaths... in fact, my all-time favourite adventure had our group (there were only the two of us, and the GM) inside a gun superstore (think Wal-Mart, but only selling firearms) that was attacked by a corporate structure. So, we're running around, grabbing the guns we need, and then running to find ammo, so we can blast these squads bursting through the ceiling. It was a lot of fun, if a bit cheesy.
We made a few decker characters, but we didn't focus too much on the decking or rigging rules, simply because they divided the group too much (and our games were a little simplistic for that). Nowadays if I were to play, I'd jump all over the role of rigger, but I doubt I would have felt that way then.
Mostly, we made cybered up characters, or magical characters (typically hermetics; the pacific northwest is filled with native american references, and we were sick to death of it - we didn't want to play a native in our games)
My favourite character wasn't one of my own (I don't remember them very well) but with a friend's - a Racoon shaman. The character was noteworthy simply because he was more RP-oriented than combat, and it was the first time his player had ever played a character that wasn't a gun nut. The only character I remember playing was a physical adept who would kill you in two seconds flat if he got next to you.
All in all, I have a lot of fond memories of the game. I bought 3E a few years back with the hopes of running a few side games for my D&D group, but upon opening the book, I realized just how complex the rules were. I had no problem with dividing the group up (there are easy ways around this, if you use "primary" and "secondary" PC's - you play your decker while the rest of the group plays members of a decker group helping out the main PC; meanwhile, the player of the decker plays a low-level runner with the PCs on their main run... it help keeps the "troubleshooter/specialist" feel of cyberpunk, anyways... you'd never see Case going on a combat run in Neuromancer, right?).
No, my big problem with the game was that I found myself thinking "There's no way I can keep track of all these rules", so I put the book on the shelf. Every now and then, I take it down and read the whole thing, and dream....
I'm actually thinking of running a shadowrun-like game using the d6 rules system, although my version would nix the races, re-work the magic system to something a bit more sinister, and up the cyberpunk feel (I agree with hound that the cyberpunk feel of the game is pretty much gone).