Yes, I've dabbled. Well, more than dabbled, in the case of the X Files. I'm a regular visitor to the Gossamer archives and enjoy flipping through a few stories every couple of weeks or so. I tried Starsky and Hutch once, but didn't really enjoy it, and recently, I flicked through one or two Dr Who fics and didn't much enjoy them either. I dabbled in Smallville fic for a bit, but many of those writers, frankly, seem utterly obsessed with sex and not much else (with apologies to any Smallville fic writers who aren't!).
So, to your questions, Helga. Yes, I probably seek out similar themes in any fandom I might choose to dabble in. I want good strong drama; something gutsy and challenging. Romance is nice, but not the main reason I'll choose to read a story. As a self-confessed hurt/comfort addict, that's my first choice of fic, and that's why I've stayed with the X Files - Mulder goes through hell and back in pretty much every story ever written. <g> Which leads me to my other criterion when choosing stories to read - I have to like the leading man.

The general context of the fandom has to interest me as well, of course, so Buffy, Angel and Charmed fic, for example, will never float my boat.
Style of writing isn't important, but quality is very important. I won't read a story that's incomprehensible, riddled with basic spelling and grammar errors, or poorly articulated.
So what does the X Files have that L&C doesn't? Well, nothing much, really. There's more of it, but on the other hand, more of it isn't very good. There's more adult stuff, but often not very good adult stuff, and I really am not in the slightest interested in slash - of which there is quite a lot.
What's revealing, perhaps, is that it's usually with a sigh of relief that I come back from X Files fic to L&C. L&C is a kinder, softer world where people generally don't mistreat or abuse each other. I can usually rely on a good standard of writing here, too. Things are a bit more hit and miss out there in the big wide fanfic world.
Yvonne