Movement (Gex 2 and 3)

General
Tail Whip

Mainly used to attack enemies, break objects and activate switches. You can perform instant sharp turns and turnarounds by tail whipping before changing directions. The extended hitbox makes collecting pickups a little easier. Can also be used to delay the sliding state on a slippery slope.

Karate Kick

Fastest form of basic movement. Learn to travel the levels with the optimal amount of kicks and use a regular jump if there's a small obstacle and you need to re-adjust. Also keep in mind that this move gives you lots of invincibility frames.

Requires running speed to be used, which is achieved by moving in any direction for about half a second or by landing while holding a direction. The latter can be useful when you only have limited space to work with. Be aware that in Gex 2, uninterrupted running on the ground for a longer period of time will give Gex the "ability" to bonk against walls.

Tail Bounce 

Highest form of basic jumping that also functions as an attack. Just like regular jumps, the height depends on if you are at running speed or just walking/standing speed before jumping. A max-height tail bounce can break the design of many levels. In the N64 version of Gex 2, a tail bounce can randomly fail, even though the sound effect can be heard. This is due to lag. Gex 3 allows ledge grabs after a tail bounce, while Gex 2 does not.

A tail bounce doesn't require an initial, regular jump. Falling off a ledge or having a karate kick interrupted by an obstacle (both of which put Gex in his falling state) allow you to perform a tail bounce upon landing as well.

Fire Fly / Ice Fly

Getting one of these power-ups increases Gex's movement speed and is required for some skips. It also grants invincibility and allows Gex to burn/freeze enemies by holding the attack button on the ground while running a full circle around them. Fly TVs can be frozen for additional collectibles, but not burned.

Advanced
TV Cancel

This is the term used for activating a TV button without being forced out of the level. It's the signature tech in Gex speedrunning and can be performed in different ways based on the TV's surroundings.

A TV Cancel within a level is commonly followed by a death abuse. The game will react the same way as it always does when you die and place you at the start of the level / the last checkpoint, but the remote will actually be obtained.

Slope/Air Jump

Super Tail Bounce

In the Circuit Central levels, there are green pads on the floor that allow you to do a special high jump if you have the charge power-up active. To perform a Super Tail Bounce, step on the pad to launch yourself up, then press and hold the jump button mid-air while moving into a wall. If done correctly, you will be launched way higher than intended as soon as you clip an edge during your special high jump.

Rope Jump

When Gex is riding down a zipline, you can press the jump button on the last 4 frames before he falls down automatically. If done correctly, Gex will jump rather than falling down. On the last rope before the dragon room in Mao Tse Tongue, this glitch can be used to land on top of the roof. From there, you can either skip opening the door or attempt an out of bounds karate kick into the area associated with the second remote.