Generally, any more than 80ms and games come tumbling down, some are more tolerant than others but that largely depends on the type of game.
I can tell you as a user who always has pings of 100+ that such a statement is amazingly incorrect. Most people are afraid of 'high' pings because they only know the basic idea "higher ping means higher lag time", but in fact, a game can still be quite functional with 15+ users whose pings are all above 300. Ask anyone who's played WoW, Warcraft III, Left 4 Dead, Demigod, or Halo on an Asian server.
Edit: I failed to address the original question about ping, sorry 'bout that.
Simply put, the higher your ping, the longer the response time to the server is. If your ping is 1000, you will have at least a full 1-2 second delay from your input on your keyboard to your character's reaction, depending on the server type of the game in question. P2P games, as I understand it, don't lower ping so much as lower the time delay by not having everyone work through the Host (which would double the distance between players, frequently). Does that make more sense?
