She's really interested in things like UFO's, ghost sightings, and the supernatural in general - so I was thinking of introducing her to Call of Cthulhu (in a modern setting)...
I liked Delta Green from Pagan Publishing as a modern CoC Setting. I don't think it is still available, however.
...but I wanted to ask if anyone had any other ideas of RPG's we could try. Ideally, it would be a game set in contemporary times with a sort of X-Files/Ghost Hunters/Torchwood sort of feel to it.
I really enjoyed playing in a Beyond the Supernatural (Palladium) campaign once, but I don't think it fits the specific sub-genre you are taking about. Tri-Tac's old Stalking the Night Fantastic might fit. The original system was over-complex, but I hear they have a D20 version out now. This is a case where the D20 version might be the better choice.