If you liked The X-Files, you should be watching Fringe and Supernatural.
I described Fringe to my husband the other day as a mixture between Alias, The X-Files and Dawson's Creek. Okay, okay, it really has nothing to do with Dawson's creek except that it has Joshua Jackson, who will forever be affectionately referred to by me as Pacey. It's a great show, with seperate storylines that you can enjoy as well as an ongoing mythology that as of yet is not too tough to catch up on. Also a safe bet for fans of Alias.
Supernatural is absolutely one of my favorites on TV right now. It's got several people who worked on The X-Files working on it, and like the X-Files manages to put out great montser of the week epsidoes while carrying a really interesting, origingal backstory that continues to progress and twist. Jared Padalecki and Jensen Ackles have great chemistry as brothers, and are just all around fun to watch.
If you liked Gilmore Girls, you should be watching Private Practice.
Okay, okay, I know that they're not really even in the same genre. But one thing they do have in common is that these shows are PURE girlyness. It takes place in a medical clinic that includes a pediatrician, and internal medicine doctor, fertility doctors, a new age doctor, and a therapist. The relationships are complex, and draw you in. Despite the fact that they're co-workers, they're a family and it's all about the talking and the secrets and the story. Give it a try!