Recs for ongoing series, sci-fi:
Fringe - The first season is somewhat slow, but it has gotten so good. It's the best genre show on TV right now, in my opinion.
Eureka - It's a fun sci-fi show, definitely campy, but enjoyable.
Warehouse 13 - Similar to Eureka (actually, the two shows cross over at one point), more of a focus on archaeological/fantasy plots.
V - A remake of the old alien invasion series. Generally solid, the first season got better as it went along.

Recs for ongoing series, general:
Lie to Me - It has a very similar dynamic to House. I only watch this one sporadically; sometimes the investigation of the week just bores me, but it can be very interesting.
Hawaii Five-0 - Law enforcement procedural, but fairly unique due to its location and premise, in which the main characters are an independent task force and sometimes clash with the police. Good actors, including Daniel Day Kim and Grace Park.
Mad Men - This is the best show on TV, period. It is consistently fantastic: writing, acting, directing, they're all superlative.
Weeds - A great show that is not afraid to make drastic changes when the plot calls for them. It's a very strange mix of comedy and drama.

Recs for canceled/finished series, sci-fi:
The 4400 - It was Heroes before Heroes existed and did it better. A bunch of abductees are mysteriously returned in the present day, not having aged, and some exhibit new abilities.
Farscape - I saw that you've tried this before and haven't made it very far, but seriously, try again. You have to put in a little energy to get to know the characters, but it definitely pays off.
Caprica - A really great sci-fi show that couldn't keep an audience, which I hypothesize is because a lot of BSG's audience was really just interested in space battles.
Buffy and Angel - If you're not opposed to modern/urban fantasy, these are probably the best in that genre. You like Firefly, so these other Whedon works should be up your alley. Also, check out Dr. Horrible and Dollhouse.

Recs for canceled/finished series, general:
The West Wing - The first four seasons are tremendously well-done. The latter three seasons take a dive in quality due to Aaron Sorkin's departure from the show, but aren't uniformly awful. (If you end up liking Sorkin's work, also try Sports Night and Studio 60.)
Veronica Mars - A show about a girl who becomes an amateur private investigator, following in her father's footsteps. After her best friend is murdered and her father, then the sheriff, accuses the friend's father of doing it and gets voted out of office, she has to deal with her plummeting social status as well as finding the real killer. It's one of the best shows ever created; witty, lots of intrigue, and great acting. I rewatch it once a year.