Kingdom Hospital and The 4400 both used the same eerie theme music.

Nothing even comes close to Harry Lubin's Theme for
Alcoa Presents One Step Beyond
. I even bought the entire vinyl album of Music from One Step Beyond. The main theme for One Step Beyond was Fear. Another good one used was Weird. He then did music for season 2 of the original
Outer Limits
. In addition, he wrote specific music for different episodes specific to the mood of each episode. I thought his stuff was brilliant.Some of these themes are still available for download from iTunes and other sites.
Check Lubin out:
http://www.imdb.com/board/20523900/

I can't believe nobody listed
TALES FROM THE DARK SIDE!!!

The theme for THE INVADERS is taken directly from an episode of the original THE OUTER LIMITS, composed by Dominic Frontiere.

I like this post.. Mine has to be the theme music for Midsomer Murders!
https://www.youtube.com/watch?v=_Sv6TO11TNg

Twilights Zone is the only one that fits how I use the word "eerie" which is a bit hard to define.
Check out the theme for the first two seasons of Sanctuary. I would describe it as: mysterious, melancholy, feminine, noble.
https://www.youtube.com/watch?v=4I14p86Vm2w

Journey To The Unknown
Thriller (UK TV series)
Both these were by Brian Clemens who always had great music in his shows (he did The Avengers too).
As an earlier poster said "The Invaders" is probably top of the list.
'Knowledge is cheap at any price'

The X Files, Dr Who (the 60s and 70s versions of the theme particularly), The Twilight Zone (Constant's season 2-onwards theme), Alfred Hitchcock Presents, I would all call eerie

Have you never heard Dominic Frontiere's music for the original THE OUTER LIMITS? It is unmatched in it's brilliance.

The Alfred Hitchcock Hour "Funeral March of the Marionettes.

I think The Walking Dead theme music was great and eerie at first. Since the first season the series itself just haven't been that good anymore..

This message has been deleted.

I have to go with Dark Shadows from the 60s/70s

Yes, the theme I was talking about is the one with guitar and bongos. It's too bad the Herrmann theme is not remembered as much as the Constant one - I myself had forgotten it when I wrote my post. I'd certainly qualify it as eerie.
I also remember really liking the score in the episode "A Hundred Yards over the Rim". I think it was by Fred Steiner.

This message has been deleted.

This message has been deleted.

The Twilight Zone - although the theme is notable in its
own right, I'm on the fence about classifying it as "eerie".
A Wikipedia writer has (perhaps a bit harshly) called Marius Constant's TZ theme
"jarring and dissonant."
But Bernard Herrmann's original TZ theme (now often forgotten?) was very different.

Twilight Zone is the only one I'd call
eerie.
Original Dr Who for
wonder.
CSI for
attention
getting, of course they had a good band behind them.