Ace-
Wakko Warner sometimes did this.
AFAIK the shtick originated with Felix the Cat and his Bag Of Tricks.
Wow, this and the She-Ra thread is a total flashback for me.
There was a cartoon that I don’t think was mentioned, I don’t know if it was “The Getalong Gang” or something having to do with a caboose. I just remember the characters hung out in a caboose and there was a moose character wearing a varsity sweater (I think) that I had a doll of.
Or maybe I’m thinking of two different cartoons altogether? Help!
Saramamlana
No the caboose was indeed on the Get Along Gang. Bunch of elementary school age anthropomorphic animals with a clubhouse in a caboose.
Pandamonium- A vilain who was an evil voicem, a pair of hands, and a purple cloak. A set of magic crystals everybody wanted. And three pandas who could combine into a superpanda.
Foofur- A blue dog and his friends have uninspired adventures.
Pink Panther And Sons- Those kids were some funky colors.
Rude Dog And The Dweebs- The Rude Dog logo comes to life as a dog with attitude. He hangs out with a bunch of dogs he rescued from the dog catcher.
Street Frogs- “Who can do a hip hop better than a frog can? Streetfrogs!”
I’d need a month of vacation time to list all the cartoon shows I remember. 
Two from the '90s:
Sam and Max
The Tick
Geez, nobody remember Davy and Goliath?
Simpsons
Family Guy
You guys pretty much hit all I can recall from the 50’s and 60’s. There was an animated Beatles cartoon show which probably was a precursor to Yellow Submarine. King Features, I think.
Did someone mention Tom and Jerry yet? It was previously mentioned, but Beanie and Cecil was one of my favorites. I remember a green plastic Cecil head/neck that came filled with bubble bath powder. When I was done bathing with it, a little surgery by my dad resulted in a Cecil Sea Serpent Bank.
I seem to remember a Green Lantern cartoon. Of course, various other DC heroes had their moments on the tube. Anyone mention Mighty Mouse yet?
I never saw Davey and Goliath, but my husband frequently repeats bits of a Mad sketch about them. It goes like this:
Goliath (deep, stupid voice): Davey. Davey! It’s time to cleanse the city, Davey!
Davey (high, screechy voice): oh, I don’ wanna!
Goliath: Come on, Davey.
Davey: Die, sinners! (comes screeching down stairs with a firethrower or something.
Odd.
Of course, the old Spiderman, and the original X-Men.
How about Peter Potomus, Tom Slick, and the Archies? Tom Slick was cool, racing in the Thunderbolt Greaseslapper saying things like “there’s no such word as give up, ‘give up’ is two words”.
Goliath: GOLIATH NEEDS BLOOD!!!
Speed Racer.
Mightor the Barbarian.
The Lone Ranger.
Hoppity Hooper.
Too many others to mention.
Regards,
Shodan
We haven’t run out yet. Here are a couple that haven’t been listed:
Pirates of Dark Water–A prince from a ruined land, a pirate, an ecomancer, and a flying monkey try to gather magical treasures that will enable them to put an end to the “dark water”, a menace that drags everything it encounters into the depths and saps the life from the land.
The Funky Phantom–An incredibly bad Scooby Doo ripoff, featuring a ghost-hunting gang that included a ghost. I only remember seeing one episode; I hope that means that someone saw what a travesty it was and prevented the studio from making any more.
People haven’t been posting them, but I saw no prohibition on modern toons for the list, so here are a few in their own section:
Courage the Cowardly Dog–A small purple dog with bad teeth defends the oblivious Muriel from the horrors that plague Nowhere, KS.
Dexter’s Lab–A young genius creates scientific wonders in his secret lab, only to have them wrecked by his older sister.
Jackie Chan Adventures–A surprisingly entertaining cartoon version of Jackie Chan, fighting to keep various magical artifacts out of the hands of the forces of darkness. It seems to stay unusually faithful to the various Asian mythologies it draws on (although it will wander away for a joke, like stealing a chiang shi’s left sock for a banishing spell).
Justice League–A reasonably entertaining superhero show featuring Batman, Superman, Wonder Woman, Flash, Hawkgirl, Green Lantern, and the Martian Manhunter. Kicks all kinds of Superfriends a$$. Little heavy on the angst sometimes, though.
Teen Titans–More superheroes, this time the (new) Teen Titans: Robin, Starfire, Beast Boy (Changeling), Raven, and Cyborg. Very anime-esque style, and considerably more lighthearted than Justice League, but it has some serious themes, too.
One of my favorite cartoons when I was a kid was one that was banned from the airwaves by the government for being just a 30 minute cereal commercial Linus the Lionhearted .
At the time I thought the cartoons themselves were just hilarious. Little did I (or they) know that the show was just a precursor to the infomercial.
As the link shows the show was about Linus the lion king of the jungle and the wacky hijinks between him and his animal pals. Of the show’s cast only Sugar Bear survived banishment. He remained the spokesbear for Sugar Crisp (later Super Sugar Crisp) cereal for a number of years.
I don’t believe anybody’s mentioned “Beverly Hills Teens.”
I vividly remember the opening animation, but not, oddly (and thankfully!) the opening song.
I hated Beverly Hills Teens.
Not quite as Bad was
Maxie-. A Barbie-esque chick, with Midge-esque and Ken-esque friends. “Maxie. Maxie. The gilr on the go. Maxie. Maxie. In her own tv show. Good times are happening in Maxie’s world.” The show had some redeeming features. Mostly Maxie’s breasts.
C.O.P.S-Fighting crime in a future time. Mostly the show sucked. But one of the guys was a mad scientist with a clear dome on his skull that exposed his brain.
Biker Mice From Mars- They were bad mamma-jammin anthropomorphic mice with My Favorite Martian antennae. They fought a bad guy who was IIRC from Neptune and secretly a fish man. Their April O’Neal companion wore a black mini skirt.
Visionaries- "Visionaries, knights of the magical light. Visionaries, with magical powers they fight. Powers of strength and skill and speed. Powers that accomplish the greatest of deeds. Visionaries, knights of the magical light. As the planet Prismos comes into the proper astrological alignment, the millenia long age of science ends. All their great technology stops working. But a new age of Magic begins. The wizard Marlynn grants 2 groups of knights (the heroic Spectral Knights and the villanous Darkling Lords) powers. In times of great emotions, they are transformed to animals.
Toxic Crusaders-Based on the classic Troma film, Toxic Avenger. Toxie was joined by Major Disaster, Nozone, Junkyard, and Headbanger. Together they stopped the alien Dr Killemoff from drestroying the environment.
Ultimate Muscle-Yeah, the cartoon only debuted in America a few years ago. But the Muscle toys were a big fad in the 80’s.
Just a couple I haven’t seen listed that I always liked – and probably a couple I didn’t:
Milton the Monster
The Hair Bear Bunch
Wacky Racers
The Perils of Penelope Pitstop
Birdman and the Galaxy Trio
The Ahrabian Knights
8th Man
(Do Puppets Count?) Fireball XL 5
Shazzan!
Lippy the Lion and Hardy Har Har
Wally Gator
Yogi Bear
Huckleberry Hound
Lone Ranger
Planet of the Apes
Ant and the Aardvark
Autocat and Motormouse
Pixie and Dixie
Snooper Cat and Blabber Mouse
Eek! the cat
The Mighty Heroes
Pink Panther
The Inspector
Atom Ant
Secret Squirrel
The Bear Cats
Here Comes the Grump
The Bugs Bunny/Road Runner Hour
King Kong
Journey to the Center of the Earth
Rocket Robin Hood
Fantastic Four
Spider-man
Superman/Superboy/Batman/Aquaman incarnations
Underdog
I remember Doctor Snuggles, vaguely. Wasn’t that the show with a character named Granny Toots or something?
Dragon Ball
Dragon Ball Z
Dragon Ball GT
Odd School that no-one has mentioned
The Superfriends, Challenge of the Superfriends - with and without the Hall of Doom - better with though.
Chilly Willy
Droopy
Sherman and Mr. Peabody
New School that no-one has mentioned
South Park
Beavis and Butt-Head