Maybe it's because I'm indecisive and greedy. Maybe it's because I like seeing evil versions of my heroes with goatees and grimaces. Whatever the reason, I can't deny it: I love parallel earths.
Coming from the comics background that I do, the first exposure I had to parallel earths was probably DC's Earth-1, Earth-2 and so on; different versions of the same planet that existed at "different vibrational frequencies" to each other, and had different versions of the same characters (On Earth-2, Superman is older - and has a different "S" on his chest! It blew my little childhood mind), but it wasn't until Star Trek's "Mirror, Mirror" episode that I completely fell in love with the concept of there being multiple versions of the same characters in worlds just slightly different from our own.
It's hard for me to explain just why the idea appeals to me so much (Or why I was so thrilled to discover that Schrödinger's cat was, in fact, not the invention of Peter Milligan). Maybe it's really is that I'm indecisive, and love the idea that any decision anyone makes can be made differently by the same person on another Earth somewhere, or perhaps it's just the basic thrill of seeing the road less traveled becoming a little less "less traveled". Nonetheless, it remains one of my favorite SF ideas, and an easy way to bypass my critical faculties (Clone Wars writers, take note). After all, who couldn't love a multiverse full of possibilities?