It really depends on the RP in question, how much of it you are using, how much you are adapting etc. One of the first RPs I ran happened because I joined a RP about Greek Gods and it was shortly abandoned after we'd all made a few posts. So we started fresh and I pulled in a few people from that RP and the general premiss "Greek gods in the modern world" was adopted but the rest was my own. I didn't seek permission from the old GM and his idea (and my following one) wasn't unique. The details of each were. So that's where one has to be careful. Are you taking NPC'S? Are you taking original setting work? Then you want to get permission. It can't hurt to ask and it can't hurt to mention "Inspired by".