Although there is a multitude of different games in different genres, there are also a lot of optimization and planning techniques applicable to many of them.

Basic techniques

Avoiding common slowdowns

Jumping

In many platform games, movement on slopes or curves is slower than movement on flat ground. This is commonly bypassed by jumping or other kinds of aerial movement.

In many cases jumping also incurs a penalty on horizontal speed. In this case minimize the amount of your jumps and, if game allows that, their height as well.

Damage knockback

If a player character can take damage in a game, it usually means it will knock it back, in some cases also paralyzing it for a short period of time. If avoiding damage doesn't seem to be feasible, you can try minimizing the negative effect by taking damage in different conditions: while airborne, while turned around, and so on.

Optimizing movement speed

In vast majority of games, simply moving forward (in straight lines for 3D games) is faster. In 3D games this also means you need to sharply cut corners, moving in a shortest possible path from A to B. However, there are exceptions.

Diagonal movement

Certain games, usually overhead 2D games or first-person action games, sum up forward and sideward movement vectors, increasing your diagonal speed above that of a regular forward movement. This can be abused if you turn the character at an angle (usually 45° to the target direction). This technique is commonly known as straferunning.

Examples: Contra 3 overhead stages, Doom.

Utilizing faster-than-running moves

Many action games (both 2D and 3D) have moves that allow you to dodge or attack in a way whose speed exceeds that of normal running, even if it means moving in a non-straight line. Carefully examine all ways of movement (especially jumps and other aerial attacks, since they are less prone to friction) before deciding on an optimal way of movement.

Examples: Ocarina of Time, Metroid Prime.

Bunny hopping

Bunny hopping is a generic technique that consists of repeated jumping in order to preserve horizontal momentum. This is commonly used in two ways. The first is avoiding downtime after a certain in-game physics event, like falling from a large height in platformer games (Super Castlevania IV) or beginning horizontal movement (Darkwing Duck). Another is minimizing friction after building up a high movement speed (Rocket Knight Adventures, Quake series and many other FPS games). More often than not it also means that the game allows jumping without horizontal speed penalty.

Building up momentum

In nearly all platformers or platform-based games that employ horizontal or vertical acceleration (you can tell it if the player character's moving speed increases as it moves in a direction), it should be possible to save time by building up momentum before you are allowed to move in a desirable direction. In practice, this usually boils down to two major examples.

Jumping before a fall

If the character's horizontal speed isn't significantly reduced during a jump, it is usually a good idea to jump just before you fall off a platform to have a higher vertical momentum by the time you clear the ledge. This is further emphasized if you need to change horizontal movement direction after you clear the ledge (but the gain can be negated if a game doesn't allow changing directions while airborne, like Ghosts 'n Goblins or Castlevania).

Running towards opening doors

If a game has doors or other temporary blockades you have to wait for (like in Metroid series), it might be possible to go slightly back and use the distance and waiting time to accelerate. This way, by the time the blockade is cleared, the character will be moving at a high speed, saving the time needed to accelerate.

Advanced techniques

Abusing hitpoint/life reserves

In a speedrun, the character's health can and should be used to speed up the gameplay if the game allows that. There are several common ways to do so.

Damage boosting

Taking damage from an enemy is often faster than dodging it. In certain cases, most notably platform games, it allows major sequence breaking as a successful damage boost propels the player character to an otherwise unreachable distance or allows it to skip an otherwise mandatory checkpoint (example: Castlevania: Symphony of the Night). Some games also have a dedicated dodging move that can be abused this way (example: Super Metroid).

Respawn abuse

If dying in a game allows you to respawn in the same stage without resetting it (or reverting to a checkpoint), it can be taken advantage of in several ways: abusing invincibility period to bypass instant-kill obstacles, climbing heights faster, crossing pits, etc..

Checkpoint abuse

In games that use several checkpoints per stage, dying just as you reach one of them can benefit you by skipping a mandatory cutscene or refilling your HP/ammo reserves.

Bypassing unwanted triggers

Many games have cutscenes or in-game events that can lead to an unwanted slowdown. In some cases there are ways to bypass them.

Moving too fast

Certain triggers can be bypassed if you don't give them enough time to initialize. This usually means hitting another trigger (commonly room transition) before the invisible timer expires by means of high movement speed.

Examples: Castlevania: Symphony of the Night (skipping Death), Super Metroid (skipping Torizo).

Moving around the trigger

In platform games, be it 2D or 3D, triggers are commonly placed as small areas of a ground activated by stepping upon them. However, it more often than not means you can move around them, commonly by jumping over/around them or using an event that instantly moves you behind the trigger.

Example: Half-Life series.

Clipping through objects

As elaborated on Bughunting, collision detection in games isn't always perfect. In certain cases it means there are ways to clip inside/through an object or terrain element by pressing into it with a certain force or under a certain angle, while under a certain movement- or collision-altering effect (such as invincibility period), by using another object, or a transportation device (often as simple as a ladder, like in NES Donkey Kong).