Non-Fatal Explosions: Mostly played straight, but averted at the end of Mouse Trouble, in which Tom dies and... goes to Heaven? Huh.
No OSHA Compliance: If an episode takes place in a factory or a construction site you can bet this trope will be in full effect.
Not-So-Harmless Villain: Tom for the large part plays the bumbling antagonist of the two. There are several times however he manages to get the upper hand over Jerry or even win on rare occasions. If pushed far enough he can even outdo Spike, who he usually cowers before (eg. "Pet Peeve", "Dog Trouble").
Off Model: Gene Deitch's cartoons suffer some pretty severe animation glitches. Probably the most glaringly obvious instance was in "High Steaks" where Tom's in a swimming pool, as the animators didn't bother animating any of Tom's body below the waterline, despite the water having been drawn in a transparent fashion.
Oh Crap: Tom gets an epic one when he's trapped in a locked room with a lit dynamite in "Cruise Cat".
Jerry at times as well, perhaps his most elaborate in "Quiet Please", after Tom drugs Spike to sleep.
In "The Million Dollar Cat", Jerry spends the whole episode smugly putting Tom through the works after an inheritance clause prevents him from harming a single animal ("Not even a mouse"). Tom finally blows a gasket, at which point Jerry, now more meek, points out the contract again...which Tom tears to shreds in front of him...
Tom again in "Love That Pup", specifically near the end when he believes he's trapped Jerry in a barrel and starts pummeling it with a shovel. Spike notices and threatens to skin him alive if it's his son. Tom at first smugly and confidently decides to lift it, only to find Jerry is out of the barrel. Que the double gulping "Oh Crap" moment when Tom realizes who is under the barrel.
The cats, namely the Butch, in "Smarty Cats". They spend the entire short watching old movies (actually past shorts) of Tom humiliating Spike. Jerry, having been kicked out of the house repeatedly because they want him watching, has had enough and pushes Spike to the window to see what they're doing. After finishing the last movie, Butch leans into someone and mocks Spike's barking. Few seconds later, his smile drops and his barks become more high pitched when he realizes he's leaning against Spike. Then all four cats panic and run with Spike chasing them.
The Only One Allowed to Defeat You: Even if Tom will team up with other cats to catch Jerry, he will NOT let them eat him. And god help you if you're a cat that tries to catch Jerry and Tom sees you doing it.
Only Six Faces: All of the characters use the exact same design, but with species specific traits and proportions applied to them. Don't believe this? Well, compare all of the characters to the seal from the short "The Little Runaway" which is basically what Tom and Jerry and the others would look like when you take away their species specific traits.
Well, at least all four-legged characters. The side effect of this is that when one character wants to disguise as another, it can be relatively easily done.
Overly Polite Pals: Tom, Jerry and Spike the dog do the routine in the 1948 short, "The Truce Hurts."
Packed Hero: At the start of "Cannery Rodent", Tom is chasing Jerry through a fish packing plant and both get packed into cans of tuna, which inexplicably has a picture of each of their faces on the packaging. Near the end of the same cartoon, a shark that has been pestering Tom for the majority of the cartoon is sent through the same packaging machine and canned in a similar fashion.
Papa Wolf: Harm, or even touch Tyke, and Spike will skin you alive!
Pet Heir: Tom in The Million-Dollar Cat (until he throws it away by violating the 'no harming animals' clause), Toodles in Casanova Cat.
Phoneaholic Teenager: In "Busy Buddies" and "Tot Watchers", the baby sitter left in charge at Tom's house goes straight to the phone right after the husband and wife leave, only leaving the phone to punish Tom for bothering the baby (when in fact he was returning the baby after it wandered off).
Pie in the Face: In "Quiet Please!", Tom catches Jerry on the kitchen counter. Jerry asks for a moment to draw up a last will and testament, in which he leaves a custard pie "to Tom, my favorite cat". Reading this, Tom eagerly tells him to "Lemme have it!"
In "Solid Serenade", Jerry hits him with two pies... one of which has a steam iron hidden inside of it.
Tom pelts Jerry with one at the end of "Jerry's Diary", after being angered by what he read in said diary.
Random Events Plot: "The Tom & Jerry Cartoon Kit" started with Tom and Jerry in a box along with an assortment of other items, including a watermelon. A narrator talks about how to make your own cartoon, starting by setting Jerry on a table and handing him the watermelon. After he spits seeds around for a bit, Tom forces him to swallow several, turning Jerry's belly into a temporary maraca. Cue dancing! Until Jerry spits the seeds out, and then finds a book that teaches mice how to use Judo...
Recursive Canon: In "Mouse In Manhattan", a theater in the background has Tom and Jerry given billing on it.
Recycled IN SPACE!: Once by Gene Deitch — who produced a short ("Mouse Into Space") that was bizarre and incomprehensible even by the standards of his Tom and Jerry cartoons — and about four by Chuck Jones which are somewhat better, but still not really very good.
And the less literal interpretation of this trope was applied all through the series, with episodes in the Middle Ages, on a farm, out west, etc. And it was employed even more often on Tom And Jerry Tales.
These appeared fairly often, including a recobbled episode where Tom watched several failed attempts to brainstorm ideas... for the same trap that failed before.
A smaller-scale one appears in "Year of the Mouse", where Tom traps Jerry and another mouse in a bottle, corks it and then ties a string to the cork that's attached to the trigger of a gun aimed at the bottle.
Rule of Funny: Tom has human-like screams and occasionally speaks in English. This is to create a deliberate Uncanny Valley, since if Tom acted like a real cat, it wouldn't be funny. Just the opposite, it would be disturbing.
Screwy Squirrel: Whenever Jerry's character starts to really lean toward this, it's usually an episode where Tom wins. A good example is "Million Dollar Cat", where Tom inherits a fortune but loses it if he harms another living creature; Jerry uses this as pretext to harass and injure Tom, then waves the telegram in his face to protect himself from reprisal. An enraged Tom, after finally realising it isn't worth the abuse, finally takes the telegram, and shoves it down Jerry's throat.
Second Face Smoke: It happens on more than one occasion — but Jerry wises up at one point and comes out of the mousehole in a gas mask, while Tom has turned green from blowing so much smoke.
Stop, or I Shoot Myself!: In the Tom and Jerry short "The Missing Mouse", Tom hears news of an escaped white lab mouse who has swallowed a powerful explosive. Jerry, who has been painted white when shoe polish falls on him, pretends to be the mouse, trying to hurt himself and forcing Tom to stop him. Eventually, Tom figures it out, and that's when the real lab mouse appears...
The 1975 version had them teamed up in every episode.
Almost every episode. At least two episodes—a tennis episode and a bowling episode—had them against each other.
Suddenly Voiced: Throughout The Movie, but also applied to the original shorts as well, though it's only done for about a line or two, and generally played for laughs. In fact, the short with the most dialogue between the two is "The Lonesome Mouse" (which understandably doesn't get much airtime).
Tom has lots of dialogue (but Jerry doesn't) in "Zoot Cat".
Tom and Jerry speaks regularly in the comic book adaptations, which had been around for decades by the time the movie was made.
Jerry is also voiced in his and Tom's cameo in Anchors Aweigh by Sara Berner.
Synchronized Swarming: The ants that invade Spike's picnic in "Pup on a Picnic" are quite organized, which helps them walk off with the entire food supply... and Spike's son.
The bees that attack Tom in "Tee for Two" are synchronized as well.
Talking Animal: Dogs, ducks, other cats and mice; although neither Tom nor Jerry themselves usually spoke. Still, it depends— sometimes they're just as mute as the title characters.
Talking with Signs: Happens occasionally. One memorable example is after Jerry stabs a box with several needles and saws it in half, with Tom inside. He looks inside the box and his eyes widen, and he quickly writes up a sign and displays it to the audience asking if there's a doctor in the house.
Translation: Yes: In "Little Runaway", the seal, through subtitles, explains his plight to Jerry and asks him for help. When Jerry agrees, the seal shakes his hand and launches to a flurry of barks. Once he's done, a subtitle comes up consisting only of the word, "Thanks!"
Even Nibbles, who isn't technically related to Jerry, looks like a smaller gray version of him.
Under The Mistletoe: In "The Night Before Christmas", Jerry stops Tom from chasing him by holding up a mistletoe and making a cute smoochy face at him. Tom then blushes and turns away shyly, only to have Jerry kick him in the rear. Truly one of the biggest Foe Yay moments in the series.
Universal-Adaptor Cast: In most episodes, they are just in some random house (usually belonging to Mammy Two Shoes or a skinny, white housewife). But then there are times where they are in the Middle Ages, the Renaissance, the future...
Visual Pun: The opening credits of "Dicky Moe" start out with a picture of Tom & Jerry in a tight spot, and the graphic "Tom and Jerry in...", then the camera pulls back to reveal they're in the titular whale's stomach.
A similar case could be made for the opening to "The Tom & Jerry Cartoon Kit".
"Timid Tabby" when Tom and his cousin disguise themselves with two heads chasing Jerry out.
Wartime Cartoon: "The Yankee Doodle Mouse" was the closest Tom and Jerry ever came to having a World War II-themed short. In it Tom and Jerry fight a war-style battle in a basement, with plenty of WWII references.
You Didn't Ask: Played with in The Little School Mouse where Jerry tries to teach Nibbles how to foil Tom and collect food, only to be foiled each time. In his own attempts, Nibbles just kindly asks Tom and he nonchalantly complies. Later Jerry tries to teach Nibbles how to put a bell on Tom. This doesn't go over very well for him. Nibbles, on the other hand, simply gives Tom the bell as a gift, and Tom happily wears it.