The NFL has had its share of ugly incidents over the years. Most of the time it's individuals doing stupid things and not wholesale riots, but as you would expect, alcohol is always a factor. The worst thing I have ever seen in person are the fights in the stands among opposing fans. This happened fairly frequently in the Dome (in the Pavilion especially and during prime time games when everyone was already drunk when they got there), and especially during games against division rivals Pittsburgh, Cleveland, and Cincinnati, but only when the Oilers were competitive of course. I was also witness to the whiskey bottle knockout of the NFL official (Armen Terzian) during the Vikings Dallas "Hail Mary" game back in the 70's. I have seen a few scuffles at Reliant the last two years but it was usually individual incidents (common to every NFL stadium) and not outlandish group misbehavior. I saw several Colts fans kicked out of Reliant in '02 for being a-holes to the people around them. That's typical and it generally happens on a small scale.
But on a larger scale there have also been plenty of group incidents lately that bother me. Hundreds of Giants fans pelted the Chargers bench with chunks of ice and snowballs a few years ago after a bad call by the referee. A Chargers coach was knocked unconscious as a result.
Then there was the incident in Cleveland a couple of years back where again, hundreds of fans pelted the field with (in some cases full) beer bottles in a game against Jax, resulting in the game being suspended for several minutes and both teams were evacuated from the field for safety reasons. This was repeated at New Orleans on a smaller scale the following night on a nationally televised MNF game.
There was also an incident either last year or the year before where security personnel had to use pepper spray on a group of unruly fans at Phillly or Washington (can't remember) and the pepper spray was spread by air handlers to the players bench.
A fan attending a game at Oakland was stabbed to death for wearing opposing team's gear. Oakland probably has the worst rep for treatment of opposing fans.
Many times the USA version of hooliganism is at it's worst during the post-championship celebrations on the streets of the winning cities (not just the NFL).
The attack by the meth-head White Sox fans is what I think people and players are most concerned about. NFL players are fairly well protected from that standpoint, but the goofball who sneaked on the field just after halftime of the Super Bowl proves that stadium security has its hands full.
The NFL is trying very hard to crack down on fan violence by revoking season tickets and working with local law enforcement agencies to issue heavy fines. It (group misbehavior) happens here, but not on what I would call a regular or predictable basis.