io9, just moments ago, published an article on resources you can use to find a gaming group in your area. They point out that finding the right gaming group can be tricky, since there's no one set of criteria everyone shares for "the right group", and your mileage may vary at all times. While this is true, I've certainly noticed a few things over the years that are important, and I thought I might share them with people.
The Big Important Points:
1) It is, fundamentally, a game. The very definition of the word "game" includes the phrase "amusement"; it is intended to be a leisure activity that you enjoy doing. This means that if anyone is taking the game so seriously that they lose sight of that--rules lawyering, losing patience with inexperienced players, being needlessly sadistic as a GM, freaking out over missed sessions, demanding strict adherence to in-character behavior, flipping out when your character dies or anything else not on this list that involves getting upset or angry over what is fundamentally a social activity--they need to relax or else they may not be a good fit for a gaming group.
2) It is a co-operative game. This is an important part of it, because while you should never lose your temper or freak out over someone playing a game badly, the counterpart of that is that you should at least put effort into it. You should try to be there for every session (yes, life happens, we all know it, but if you're missing more than one out of every five or six sessions you should look into why); you should always pay attention to the game--phones put away and TV off is a default minimum, but more generally you should listen to what everyone is saying and try to play along so long as they're suggesting something even reasonably fun; and for Pete's sake it is not a competition. Unless it is a clear, agreed-upon-by-all-parties-especially-the-GM, official and well-understood part of the campaign, you should never ever ever ever ever EVER be screwing around with your fellow party members. Basically, if everyone wants to play 'Paranoia' or something, that's fine, but that one person who always plays a Chaotic Evil character so they can backstab another player and claim "I was just being in character"? Kick 'em to the curb. They're toxic, they will ruin everyone else's fun, and they're unlikely to change.
Oh, and if you're a GM, you should always try to apply the rules in a way that makes the players' experiences fulfilling. This doesn't mean Monty Haul gaming; being challenged is exciting and overcoming a big challenge is thrilling, and that's part of a fulfilling gaming experience. It also isn't exactly the same thing as "applying the rules fairly"; sometimes the rulebook gets in the way of a fun game. (And sometimes your adventure notes get in the way of a fun game. Learning to improvise with what's interesting to your characters is a big part of making a good game.) But you shouldn't favor anyone unduly, you shouldn't disregard the rulebook solely in order to do bad things to players, you should be willing to change your mind when a player points out a legitimate rules mistake instead of getting defensive (sometimes the rules lawyer is right!) and you should always give them a fighting chance. And most importantly, you should communicate with them in a mature fashion in order to avoid misunderstandings.
That's my criteria for what makes a good gaming group. You could probably distill it down further to "Everyone should work hard to try to make everyone else's experiences fun", I suppose, but I wanted to mention specific red flags that come up when that isn't happening. Even the red flag-items, though, aren't automatically bad. As long as everyone is relaxed, participating in a spirit of good-hearted fun, and willing to take the unusual in stride, the occasional intra-party kill or GM fiat isn't going to hurt anything. Just try to remember that the point is to create good memories, and those happen whether or not you "win".