I don't know about gladiators, but chariot racers certainly did. The famous case is the Nike riots. Fans organized into colored groups, each supporting different charioteers - Blues, Greens, Reds, and Whites.

By 532 CE in Constantinople these teams had also adopted political and religious affiliations. There was plenty of hooliganism between these different groups, and in 532 several fans were supposed to be executed. Two men, both a Blue and a Green, escaped and at the next set of races the crowd called on Justinian for mercy.

When Justinian didn't act, the Blues and Greens turned hostile and rioted for five days, effectively burning down half the city, and demanded Justinian to abdicate. Justinian ended up using the army to quell the rebellion and some 30,000 people were killed.

The execution of the fans might have been the trigger for these riots, but as I mentioned earlier these groups had taken on political affiliations as well as sport affiliations, and Justinian had been employing administrators that imposed unpopular taxes to fight an unpopular war against Persia.

Here are two articles easily accessed that describe these riots. One from the Smithsonian Magazine, and one from the Australian journal Clio. They'll give you the bibliography of the secondary scholarship. The ancient source is Procopius, History of the Wars. Here is his account from the Internet Medieval Sourcebook.

It's worth noting that, judging from The Secret History, Procopius hated Justinian and especially his wife Theodora.