Here’s one written by Mark King & Mike Lindup (of Level 42 fame - one of my favorite groups). Not brilliant quality, but you get the idea …
The Steam Video Company :-
One of my favorite sitcoms:
Roadrunner
Since we’ve clearly just degenerated into posting any TV theme song, I will contribute the original Transformers theme, and a second video explaining just how bizarre it is, musically.
A couple from the past, Hercules and Spiderman, both from the late 60’s, early 70’s.
At the tender age of 8, we thought changing out the Hercules lyrics to “fighting for his life, with a plastic knife and the strength of ten plastic army men” was classic comedy.
The Mighty Hercules theme song was sung by Johnny Nash…
Instead of “Fire in every part of the Mighty Hercules,” we always sang “Fire in every fart.” 
The second I hit play on the Patty Duke theme I was instantly transported to 10 year old me, in the house I grew up in, sitting on the couch watching this. It was the last thing I’d watch before going to bed (but mom would usually let me stay up a few extra minutes until the Alfred Hitchcock Presents intro played)
Speaking of which:
A few more of my favorites. I realize sentimentality may be playing a bigger role in picking them than I realize.
My favorite Hitchcock episode will always be “Lamb to the Slaughter” with Barbara Bel Geddes (aka “Miz Ellie” on Dallas).
No love for Puffin’ Billy?
My claim to fame is hitting him right square on the forehead with a ping pong ball on live TV.
At the very end of the Hercules song, Herc yelled out a long word or short phrase which was hard to distinguish, esp after Johnny Nash’s excellent enunciation (the linked video cuts out before the yell). A mother wrote a letter to a columnist at the local Chicago newspaper (I think it was the Dorsey Conners column) saying, “After watching the Hercules cartoon, my young son runs all around the the house yelling ‘Hold on, Pierre!!!’ That can’t be right! What on earth is Hercules saying???” The answer was, “O-lymm-ppia!”
Well, we seem to have very limited restrictions as to what we identify as a theme: we have openings, closings, and character specific ones listed. As well as instrumental and non-instrumental, so I figured I’d contribute a few, starting with a few western ones.
First, I cannot (!) believe no one linked this one in the approximately one year the thread has been open!
I mean, really? It’s a great tune, evocative, and the music and imagery has been used enough in various other situations to be all but it’s own trope (and may well be, I won’t bother to go checking).
Second, from the amazing Batman The Animated Series
Moving music, which combines perfectly with the visuals to fully evoke the world. Although a bit of a cheat since Elfman was involved and it was designed like the show to evoke the live-action movie.
While I’d probably not identify it as a “best” I’m glad StarBlazers theme was linked upthread, because I’ve always had a fondness for it, and as a similar example, I’ll link the Robotech Theme that was always moving for me as a tween.
Last, two lovely pieces from anime TV series that I always enjoy but may be much less familiar to readers who aren’t fans of the genre.
From Record of the Lodoss War Chronicles of the Heroic Knight (TV series rather than OAV to keep in line with the OP)
Although almost all of the themes from the OAV are frankly amazingly evocative.
And last, but certainly not least, the full Theme from the Anime Spice and Wolf
I think these are unique to the thread thus far. In roughly chronological order, don’t hold me to that:
The Flintstones
The Fugitive
Green Acres
In The News
The Love Boat
Buck Rogers in the 25th Century
The Powerpuff Girls
And another “I can’t believe it wasn’t in this list”
Del Shannon’s amazing Runaway for Crime Story.
Good one! I loved Crime Story; too bad the second season sucked. 
The instrumental is nice, but I prefer the sung version from the pilot. In the regular series, they played a truncated version during the end credits. Although I really wish they had gotten a baritone or a bass to sing it.
That’s a nice version. Fun fact: Kipp Lennon performed the Michael Jackson singing parts in the Season 3 Simpsons episode “Stark Raving Dad.”