I pull things out of my ass. No, seriously. Nothing really "inspires" me to write an RP, I just get an idea in my head and think "Damn, that'd make a nice roleplay". Sometimes the RP itself has some influences (such as Riders in the Sky taking some aspects from Firefly), and sometimes it's completely of my own creation (Nightlife). For the most part, my RPs tend to be experiments in what people like or would enjoy playing. As such, I don't get too down when an RP of mine "dies", as that is the nature of everything. Birth, Life, Death.
Of course, as with anything else, exceptions are made. Sometimes I'll draft up a character that I really connect to and then an RP is born from his or her backstory. Sometimes I'll hear a song and a certain theme just sticks in my brain and I'll write something up about it. I get more inspired from works that grab hold of me and don't let go. Riders in the Sky was as much a nod to an old space cowboy RP I took part in as it was a desire to tell Isaac Larsen's story. Inspiration, when it comes for me, comes from many places.