I occasionally record my shows to sell. Most of the time I just offer it as an option to the member who bought the show in the first place, since most of my shows are 1-on-1 and involve use of names and other chatting that won't be super interesting to others.
I copy and save chat sometimes (usually to member notes) so I'll be able to remember certain details someone tells me, and to recall what kind of show I did.
I don't do anything for any legal reasons, but I do make sure to type rather than speak responses and usually keep notes or send a report when I'm asked to do things that break the rules of the site I'm on, so that the way I responded is on record. I don't think I've ever needed to use any of it, but it makes me feel safer in case at some point someone decides to report me.
Some sites definitely keep chat/video records in order to be able to review any incidents that come up, but I'm not personally sure of the extent. Wasn't an adult camsite, but I was recently emailed screenshots from a stream I did, as "evidence" of my supposed rule-breaking.