The Twlight Zone. The HD-origin remasters in the Definitive Edition season sets look fantastic and I'd imagine they would be spectacular in 1080p (1.33:1 windowboxed of course).
Maybe also The Outer Limits (original series). Conrad Hall shot a lot of the episodes and the cinematography is awesome.
After watching The Simpsons Movie in BD it would be great to see what they could do with the series if remastered in 1080p, as long as it's OAR.
I'll second The Twilight Zone.
For me to seriously consider repurchases I'll have to see a serious improvement in the way they plan and execute releases:
—Restoration and remastering is a must. —Videotaped shows will gain no increase in picture quality, so just try to see how few discs you can comfortably fit entire series —They should consider entire series at once.
What would be more relevant though is to ask which series which exist as 35mm negs would we like to see on HD. Most shows since the mid to late 80s whilst being originated on 35mm were edited on tape/in the video domain.
Hence whilst it might be theoretically possible for some of these to be "remade" in HD eg ST:TNG, I suspect that it simply wont happen for shows which dont have a track record of sales sufficient to justify the massive costs of doing this.