Adaptational Villainy: DTZ, the shapeshifting alien from the episode "Dale Beside Himself," did try to get Dale stuck in space, but he wasn't really evil, he just preferred staying on Earth. In the game, he's a recurring mook working for Fat Cat.
Animals Not to Scale: Both variants. Outside of some bosses, every enemy in the game is roughly chipmunk-sized regardless of species, including cats, mechanical bulldogs, weasels, and, most bizarrely, rhinos. On the flip-side, Fat Cat is downright enormous in the first game, taking up most of the screen.
Ascended Glitch: In the first game on rare occasions thrown blocks would fly in a zigzag. It became a chargable attack in the sequel.
Cartoon Bomb: Can be found in some stages and used as a weapon.
Crate Expectations: The first game had crates as a primary means of defeating enemies (either by throwing them, or hiding inside and waiting for an enemy to trip over it). They came in two varieties — disposable wooden crates and stackable metal ones. All small enough for a chipmunk to lift.
Macro Zone: "Naturally tiny character for whom every zone is a Macro Zone" variety.
The game has a rather odd scale, though. Some of the levels (particularly the ones where you interact with human-sized objects) make it look like the characters are much smaller than chipmunks, more to the scale of insects, such as Fat Cat's Casino, where the slot machines and tables appear human-sized.
Mobile Shrubbery: You can duck while carrying a box to hide from enemies. The presence of blinking chipmunk eyes on the box does not give away your presence, amazingly enough.
1-Up: In the first game, these come in the form of flashing stars that waft onto the screen once you've collected 100 flowers. In the second game, they're often placed in hard-to-reach spots.
Ratchet Scrolling: Used for puzzles in some stages, such as finding a way to obtain a not so obviously accessible 1-up without letting it scroll off the screen.
Rescue The Princess: The main plot of the first game is to rescue Gadget. This notably doesn't start till after you've beaten the first level where the goal is to find a lost kitten (which it turns out was Fat Cat's way of distracting you), and the game goes on for three more levels after you rescue Gadget.