What makes a good PnP RPG system?
These days my pet peeves are games with a million books, so if I was going to lay down a fat fifty, I would want it to be as complete as possible.
Not necessarily the PHB and DMG in one, if I like it enough to GM, I'll buy a second book, but the core book needs to be complete, not referencing other books or requiring additional purchases just to play.
I am guessing from the thread title that you are asking for a bit more than just what a core book should contain though, what makes a good PnP RPG system is a bit more all-encompassing.
I'll start backwards, with things I've found that I didn't like, hopefully that will be helpful.
Character classes who play in other realms from the party: The cyber guy in the computer, the spirit guy in the happy hunting grounds, etc. RPoL is the place for characters like this, PnP, I assume, means face to face, I don't want to sit there for an hour while the other players are off having adventures I can't be part of.
Character classes who are at odds. Some want to reveal the secret to the world, some want to keep it hidden, that sort of crap. It's tough enough finding a party that can stick together without a built in reason for them to be fighting each other.
Too much (or too little) fluff. Some games I've played in have had such a rich and rigid story-line there was no place for the players to go. One even put out updated histories which could make everything your party had done obsolete. You either have to imagine it didn't happen or you can't use the new fluff. Conversely (and I am referencing first ed. Traveler here) almost no fluff at the all, the GM was pretty much expected to generate everything from scratch. Never had more fun rolling up characters, but the game was almost impossible to play.
Stopping here, I'll wait and see if any more input is requested...