Clearly, I’m younger than most of the people in this thread.
Some themes I remember from my childhood:
Robotech (I added lyrics as a kid.)
Transformers
Gummi Bears (’…bouncing here and there and everywhere, high adventure that’s beyond compare…’)
GI Joe - nobody else like the Real American Hero?
Spiderman
I like the grandiose themes of 80s primetime soaps, like Dallas and Dynasty. For me, the theme from West Wing is reminiscent of those.
The King Kong cartoon
King Kong ten times as big as a man
Tetsuwan Atomu/Astro Boy!
There you go Astro Boy,
On your flight into space,
Rocket high!
Through the sky!
What adventures soon you will make!
(Everyone in Japan still knows this song!)
More recently, the X-Men cartoon theme.
I’d second the Robotech theme, but it’s sadly been driven out of my head by the original (Japanese) Macross theme. Fortunately, there’s a clip available at the Robotech.com site…
George, George, George of the Jungle
Strong as he can be
George, George, George of the Jungle
Watch out for that tree.
Scooby Dooby Doo
Where are You?
We’ve got some work to do now …
… and I forget the middle part …
If we can count on you,
Scooby Doo,
I know we’ll catch that villain!
I’ve also been known to hum George, George, George of the Jungle.
Ah! The classics.
26 posts and nothing for the old Bugs Bunny show??“Overture, <something> the lights, This is it, the night of nights, No more rehearsing and nursing the part, We know every part by heart!..” Now THAT is a theme song!
Spider-Man, Spider-Man. Does whatever a spider can.
Spins a web! Any size! Catches thieves just like flies!
Look out! Here comes the Spider-Man!
Is he strong? Listen, bud: he’s got radioactive blood!
Can he swing- from a thread? Take a look- overhead!
Hey, there… there goes the Spider-Man!
In the chill of night- at the scene of the crime.
Like a streak* of light- he arrives, just in time!
Spider-Man, Spider-Man. Friendly neighborhood Spider-Man.
Wealth and fame, he’s ignored: action is- his reward!
To him…
Life is a great big bang-up! Where ever there’s hang-up-
You’ll find the Spider-Man!
(*) or is it “beam” of light?
Also:
Flintstones! Meet the Flintstones!
They’re a modern Stone Age fam-i-ly!
From the – town of Bedrock
They’re a page right out of his-to-r!y!
Let’s ride – with the family down the street!
Through the – courtesy of Fred’s two feet! (ta da da DA)
When you’re – with the Flintstones
Have a Yabba Dabba Doo time
A Dabba Doo time
We’ll have a gay old time!
I sing a really good Vegas lounge/Rat Pack-style rendition of the Spider-Man theme. Performed it at the 2000 San Diego Comic Con, I did.
Ulysses 31
http://www.sfxb.co.uk/animated/ulysses31.html
How did it go? I can’t remember.
Ohmyghod, that site has the lyrics for The Littlest Hobo!
I owe you a damnfine bottle of beer. 
Thunder, thunder, thunder thunder-CATS!
Tom Slick,
Tom Slick
Let me tell you why
He’s the best of all good guys
Tom Slick,
Tom Slick
In the Thunderbolt Grease Slapper
when he’s on your tail…
You cant stop him cuz he cannot fail.
Tom Slick,
Tom Slick!!!
Mission: Magic by Rick Springfield.
Kidd Video
Marshall, Will and Holly,
On a routine expidition…
<snip>
AAAAAAHHH!
etc.
Hey, hey, hey! It’s Faaaaaaaat Albert!
Voltron: Defender Of The Universe–" Ready to form Voltron! Activate Interlock! Dynatherms Connected! Infracells Up! Megathrusters are GO!"
BattleStar: Galactica: TOS–great theme song.
The Peter Gunn Theme was from a very early TV detective, & is a classic. I nominate this for Best Instrumental Themesong.
I hope you mean “Speed of lighting”
"When in this world
The headlines read
of those whose hearts
are filled with greed
who rob and steal
from those who need
to right this wrong
with blinding speed
Goes Underdog (underdog) Underdog (underdog)
Speed of lighting, roar of thunder
fighting all who rob or plunder"
Anyone remember Funky Phantom
“He was a ver-ver-very Funky Phantom
he pops right in just when we need him most
with his cat Boo, and you can’t do without him
the cat and that Funky Phantom ghost”
Danger Mouse had a really cool theme. And it’s out on DVD, too!
Also, every time I think of the Teenage Mutant Ninja Turtles. I get the cartoon theme stuck in my head.