As an 80's child I watched a whole lot of fun cartoons.
I am going to collect intro's to them here so this will not be complete in a day or 2.

Paw Paw bears http://youtu.be/tjkkMtMJxc4
Wuzzles http://youtu.be/o1VcMYCCkSA
Denver, the last dinosaur http://youtu.be/sLlibrF5DRM
Gummibears http://youtu.be/jWigVVh7OXM
Thundercats http://youtu.be/CjaTkPYzK00
Teenage Mutant Ninja Turtles http://youtu.be/FKz2Beyb1c4
He-man and the Masters of the Universe http://youtu.be/VnBbW3g5y5Q
Ghostbusters http://youtu.be/WYgO8LWKH4I
The Real Ghostbusters http://youtu.be/M7VS-ZoeMqs
M.A.S.K http://youtu.be/o2Z1yLO9C-Q
Bravestar http://youtu.be/_n40Un4GP6E
Swatcats http://youtu.be/K_AdxJWFUh4
Samurai Pizza Cats http://youtu.be/WZNt9p4LWeA
Ducktales http://youtu.be/VAAKU9UxOeU
Animaniacs http://youtu.be/CWnWwN1z_UM
Tiny Toons Adventures http://youtu.be/3EiEX4tmCfY
My Little Pony http://youtu.be/oqpV_JP4UVo
JEM http://youtu.be/aRyDxEBiQUY
Transformers http://youtu.be/aASYfqP9414
Captain Planet http://youtu.be/DMoodiD0UEI
G I Joe http://youtu.be/gc8mVs2H4Vc
COPS http://youtu.be/Dy4YFDSDW4w
Dinoriders http://youtu.be/tpuhLkh358Y
Captain N http://youtu.be/RyoUecpe_wU

To look up:
Buck O'Hare
Super Mario Bros
Dinosaurs
Diplodo's
Beetlejuice
Bionic Six
Jace and the wheeled warriors
Bikermice form Mars
Muppet Show
Fraggle Rock
Muppet Babies
Biscuits
Shirt Tales
Paw Paw Bears
Beverly Hills Teens
Spiderman and his Amazing Friends
X-men
Batman
The Mask
Visionaries
Heathcliff
Dennis the Menace
The Smurfs
Snorkels
Teddy Ruxpin
T-rex
Reboot
Dungeons and Dragons