Also if you were too old to do slow motion Six Million Dollar Man fights, you didn’t live…
Though rolling around on big wheels playing Rat Patrol was probably fun too.
Giiligan’s Island has to be on the list for it’s lyrics. Peter Gunn is the best. Hawaii 5-0 comes in second.
Others to consider, Mr. Ed, The Garry Shandling Show, The Beverly Hillbillies.
OK this is a wide topic. I’m gonna make an executive decision from a position of no authority at all, that 3 is not enough and I’m doing 5.
Batman
The Munsters
The Avengers (60s)
National Geographic Specials (60s)
ABC Movie of the Week (Bacharach theme or “Nikki”)
Honorable Mention: The Name of the Game, The Prisoner, Room 222, Wild Wild West, Mission Impossible, Perry Mason, Underdog, HR Pufnstuff, Josie and the Pussycats, Hawaii 5-0, The Bold Ones.
You’re never too old for a slow-motion Six Million Dollar Man fight! :o
Peter Gunn The winner in a landslide.
Hawaii 5-0 (the original)
Mission Impossible
Those are all instrumentals. If I had to pick best lyrics, it would be harder.
Perhaps Welcome Back Kotter
Worst lyrics might go to Bonanza. You’ve probably never heard them, but I’m sure Lorne Greene “singing” the theme must be on the interwebs someplace
I’ll see your Gilligan’s Island and raise you Hogan’s Heroes (with lyrics!) 
In no particular order:
Barney Miller
Firefly
MASH
Ah, but WHICH L&O? the original long one, the mid-run shorter version, or the Power Version from the last seasons?
*The Odd Couple *(original)
*Peter Gunn
Alfred Hitchcock Presents
*
Or, you may prefer Johnny Cash:
Hawaii Five-O with lyrics!
Don Ho:
Sammy Davis, Jr:
I like the instrumentals myself.
My picks are:
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The Lone Ranger (it is a part of an acclaimed classical orchestra piece after all but most people still immediately associate it with the Lone Ranger).
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Hawaii 5-0
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The original Dallas
Intros with vocals are harder but there are some very memorable ones. I think a good intro song can’t stand on its own. It has to instantly evoke memories of the show even decades later.
Here are some that do that well:
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Cheers
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The Addams Family
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Gilligan’s Island
Other contenders are The Fresh Price of Belaire, The Mary Tyler Moore show, The Brady Bunch, Friends and The Greatest American Hero
Gilligan’s Island
Cheers
Mission:Impossible
The Persuaders (1971)
***The Prisoner ***(1967) Also one of the best lead-ins **ever**!
The Protectors (1972) (with lyrics)
The Avengers
Sanford and Son (“Streetbeater”)
The Bill Cosby Show (1969-71) (“Hikky Burr”)
Honorable Mention: Perry Mason
- Doctor Who* (during the Peter Davison era)
The Texas Wheelers (John Prime’s “Illegal Smile,” a song about smoking pot. Why this was chosen for the theme of a family comedy is anyone’s guess) John Prine - Illegal Smile - YouTube
Red Dwarf “it’s cold outside/there’s no kind of atmosphere …”
The Rockford Files with answering machine
And of course the bouncing ball and AUUGAAH of My Mother The Car
I’ll see your Peter Gunn and raise you 77 Sunset Strip:
Bonanza - with lyrics!!