I had been strongly tempted to answer "Alexander McCall Smith" for this part of the tag, but The Soliloquist has beaten me to it.
While Smith does still remain a contender, I think the two most favourite (and intriguing) titles I have come across are from two extremely famous plays - Who's Afraid Of Virginia Woolf by Edward Albee and A Streetcar Named Desire by Tennessee Williams. When I'd heard of them, my curiosity was aroused and I just had to read them. In particular, the curiosity about Williams' play was piqued by the fact that I'd once read an Archie comic, in which Veronica Lodge said, "Why would anyone name a streetcar, that too 'Desire'?"
I'm very pleased that we're going to study them this semester - they're both brilliant plays and it's a rewarding experience to read them. :)