Absentee Actor: The two dogs were absent in "Substitute Teacher" until the very end, and even then only the Little Dog has just one line.
Adam and Eve Plot: This happened at the end of the episode that spoofed Noah's Ark. After eating all of the food on the Ark, chewing off the horns of the unicorns, and other disasters, Hollywood/Noah finally gets sick of the dogs and tries to throw them overboard. Suddenly the storms passes and an overjoyed Noah shouts "Drop anchor, brethren!" Big Dog then throws the anchor in the air, sinking the ship. The Dogs end up swimming to a nearby island. Thousands of years later all of civilization looks like the two stupid dogs. It's probably best not to think about which dog was the "Adam" and which was the "Eve".
All Just a Dream: Played in an interesting way in one episode. They thought they were in a dream, and tried to wake up from it no matter what. It lead to alot of pain at one point.
Boot Camp Episode: They were sent to "cartoon boot camp" and given the names "Hammy & Loafy".
Catch Phrase: Hollywood's "Well, isn't that cute... BUT IT'S WRONG!!" Subverted exactly once in the series with the episode "Love" — Hollywood even broke the Fourth Wall to deliver a Lampshade Hanging.
Genre Savvy: Even stupid dogs can have a bout of Genre Savviness. The third time they meet Red the little dog tries to get away from her calling her an "evil little girl" after the last two times they met ended badly for them. Of course they are once again tempted to follow Red by the dog food she is carrying.
Incidentally, this was also the episode that actually ends well and they all lived happily ever after.
Most Definitely Not a Villain: Little Dog's plan to distract a cat was using a cat puppet. "Hey, cat! Hey! Look at me! I'm a cat, not a puppet! And we can be friends, you can trust me, because I'm a cat, not a puppet... and definitely not a dog."
Naked People Are Funny: In the episode "Stunt Dogs", when Hollywood accidentally gets his loin cloth torn off.
Hollywood: now wasn't that cute... BUT IT'S— *revels to have a pineapple covering his crotch*
No Name Given: The eponymous dogs. They are called Big Dog and Little Dog. Though in "Cartoon Canines", they are called Loafy and Hammy, respectively. But in "Love", a female hamster calls Big Dog Jonathan. In "At the Post Office", in order to play it safe (he didn't know his own age), Little Dog decided to fill a draft form and didn't know his own name. Based on Big Dog's last answer to the question about his name, Little Dog registered his name as Ida Know.
Perma Stubble: Hollywood, even in the episodes where he plays a woman.
Pet the Dog: On one episode, the bully who torments Kenny Fowler gives him chocolate malt balls through the computer while shocking their substitute teacher (Mr. H).
Pie-Eyed: Used in "Hobo Hounds", which was made to look like an old silent cartoon.
Puff of Logic: Secret defeats a living quark by showing him via a dictionary that he is purely a hypothetical particle and thus doesn't exist.
Used as a Running Gag in the episode with the not-Brady Bunch, with the father regularly asking the kids what they learned from various events during the episode, only for them to keep coming up with Non Sequitur aesops.
One episode in Vegas has the dogs only want to go to a casino's hot dog buffet. However, Big Dog wins a huge jackpot in the slots prompting the casino's owner to force them to gamble in order to get his money back, but they end up nearly draining the casino dry of money instead. Eventually the Big Dog loses after the owner agreed to give the two all the hot dogs from the buffet in exchange.
During the The Price Is Right spoof the little dog keeps trying to lose every round because he wants the consolation prize box of doggy treats. Naturally he wins every round. Taken to a truly ridiculous extreme when the dog sabotages the final round to avoid winning the grand prize — a luxury car. The host calls him out on cheating and makes him take the car.
Why Do You Keep Changing Jobs?: Hollywood. Taken to the extreme in the "Pie In The Sky" episode where the dogs visit every department of a store, and the salesperson in each and every one is asn identical twin of Hollywood in different clothes.
He's not the only one. The store clerk seems to be employed by every existing store in the show as well.