I almost did this as a single shot post, and then realized “no, you fool, there is potential to stretch this out so people who don’t like computers, curmudgeonliness, or economics will still read the blog!” So, I am stretching this out. You’re welcome.
My criteria:
1) Show must be clearly identifiable as science fiction. I do not like fantasy in my science fiction, nor science fiction in my fantasy. You can have space ships and robots or you can have dragons and swords. You cannot have both. I am very firm on this point.
2) Shows with a significant science fiction subplot are excluded, no matter how awesome. I’m thinking here of Buffy the Vampire Slayer/Angel (the Initiative is definitely sci-fi, and Fred, at the very least, has sci fi moments) and Lost.
3) For the actual top fifteen, I had to have watched the vast majority of the series. I’ll relax that in this post, and this post only.
4) I have to have seen it, obviously.
On to the Honorable Mentions!
Twilight Zone — I’ve seen a handful of episodes, but only a handful. I may rectify that some day, but I haven’t yet.
Star Trek: Deep Space Nine — The opening music was fantastic. The show, less so. It wasn’t bad, I just don’t have a clear mental picture.
Hitchhiker’s Guide to the Galaxy — Too short, but what is there is genius.
Red Dwarf — I’ve seen the first couple of episodes, but have decided to watch it with the wife and so I can’t say more.
The Original Star Trek Series — I think I’m alone in this, but it just doesn’t hold up well for me.
The Six Million Dollar Man — Great show, but kind of light on overall plot.
Star Trek: Voyager — I am forever scarred because this series was the first time my dad decided to comment on a woman’s figure — specifically, Seven of Nine.
These will come out regularly — several times a week. If I think of new stuff to add to this post, I’ll add it here.
36 Chambers - The Legendary Journeys: Execution to the max! 
Interesting series idea. I’m going to wait until you’re done with yours before coming up with my list. I expect that we’ll have quite a bit of overlap.
I want to point out now for posterity’s sake that I have completed my set list. I don’t have an ordering yet but I do have 15 shows of my own, as well as a list of shows that I’ve heard good things about but never actually watched.
Incidentally, my vision of sci-fi will be a bit looser than our resident Penguatroll’s—Buffy will be on my list. There’s another show I really loved but am having a very, very hard time slotting it in as science fiction, as it kinda-sorta had a “five years into the future, permanently” vision.