The Latin Mass, for starters. They do not recognize the post Vatican Council II liturgy. Like it or not, it's here to stay.
I do know some people believe that only the Tridentine Rite is valid (not even the Byzantine or Armenian Rites). That is more provincial ignorance than anything else.
I don't buy the arguments that the Novus Ordo Missae is invalid (all the right stuff for the consecration is present), but I never know what I'm going to get with it. There are really good, reverent priests--and then there are electric guitar Masses and processional sambas. You're probably right that it's here to stay. I just wish they'd come out with a version of it that's less easy to desecrate.