Roman theater?

I have read that theater was banned in Rome, but then I keep running across references to Roman theater. Was there theater in ancient Rome? If so, has any of it survived to the present?

What you probably came across is that theater as a physical place was banned: the senate opposed the building of permanent theaters, which indeed weren't built until the late Republic. Before then, Rome had temporary wooden theaters.

So yes, of course Rome had theater.

The Romans did indeed have drama. There was apparently some Italic tradition which was strongly influenced by contact with the Etruscans and Greeks.

The first Latin playwrights known were Livius Andronicus, Naevius, Ennius, and Accius. The oldest that have survived are comedies of Plautus and Terence. All wrote in the mid 3rd to 2nd century BC.

It is also true that the Romans long distained permanent theater buildings. Temporary structures were built for each festival and pulled down afterwards. Evidently the Romans thought permanent theaters with seats were too "Greek" and subversive for good Romans. Pompey's theater, built in 55 BC, was the first permanent theater in Rome.

"A Funny Thing Happened On the Way to the Forum" is loosely based on some of Plautus' plays.