Gem

Gems are collectible stones that appear throughout the Crash Bandicoot series. Gems are typically different than the power crystals, as in they are more powerful than the crystals if all of the gems are collected as stated by N. Brio in Crash Bandicoot 2: Cortex Strikes Back. Whether that information is accurate is questionable as it seems that Uka Uka wants the crystals more than the gems since Crash collects these throughout the series. They are usually collected through different means and special tasks like breaking all the crates in a certain level. The gems also appear in different colors, which are more special and rare than the regular gems. In Crash Twinsanity there are six gems hidden in each level for Crash to collect which count towards 100% completion.

Overview
The gems appear in every main Crash Bandicoot console game to date. They are typically collected in every level that contains a crystal. The gems are different from crystals though. Crash is forced to collect the crystals in every level in order to advance in the game and plot, but gems are more optional for him to collect. However, they are still required to collect if the player wants to reach 100% completion.

Clear Gems
The most common way to collect gems is by breaking all the crates in a specific level. This requires Crash to go out and search every route and complete every bonus round to ensure that he earns the gem at the end of every level (except in Crash 1 where crates in bonus rounds don't count towards the crates in the level). There are also different methods to collect the normal gems like completing a death route, completing a specific task, or completing a secret level.

Colored Gems
Colored gems are similar to the regular gems, but function differently and are more rare. There is only one of each color gem in every Crash Bandicoot game and the common colors include blue, red, green, purple, and yellow. The colored gems usually require a different and more difficult task to obtain them. Most often this is beating a death route, but it also can be scouting a secret area of the level or completing a special task for a certain level. Once a colored gem is obtained, it is counted towards the regular gem total.

The difference between the colored and clear gems is that the colored gems provide a special lift in certain levels once they are obtained. These special gem lifts allow Crash to access different areas in a level in order to break more crates he couldn't break earlier or take him to a completely different route to collect more clear gems. These gem lifts will only work once the color gem has been collected though. Otherwise, only an outline of the lift will appear if the gem has not been collected yet. In Crash Bandicoot: The Wrath of Cortex, in any level that has a colored gem, the secret path to it will become outlined if the player has died anywhere but the special areas.

What follows is a list of each kind of gem and where they can be found in the various games.

Crash Bandicoot 2: Cortex Strikes Back
Obtaining all gems is one of the requirements for 100% completion and the second ending.

Crash Bandicoot 3: Warped
Obtaining gems is one of the requirements for maximum 105% completion and the second ending.

Crash Team Racing
In this game, there are five colored gems: blue, red, green, yellow, and purple. Each of these gems is acquired by winning the corresponding gem cup. The gem cups are unlocked by obtained all CTR tokens of the same color. Obtaining all give colored gems unlocks Turbo Track.

Crash Bash
Each minigame (except boss fights) contains a green gem. These are the only gems in the game. They are obtained by either winning a round in a short amount of time, or with the odds against the player. Gems are required to unlock boss fights and move on in the game. 25 gems are required to unlock Keg Kaboom.

Crash Bandicoot: The Wrath Of Cortex
Obtaining gems is one of the requirements for maximum 106% completion and the second ending.

Crash Bandicoot: The Huge Adventure
Obtaining gems is required to access the Mega-Mix hidden boss fight in which the final clear gem can be obtained and the second ending.

Crash Bandicoot 2: N-Tranced
In this game, all clear gems are obtained by breaking all boxes in a given level. There are three secret levels unlocked by obtaining all gem shards of a given color (and level theme) which are hidden in most platforming levels. These secret levels each contain a colored gem. To enter N. Tropy's boss fight, Crash has to obtain the three colored gems. Each of these colored gems is required in order to play the time trial in the respective level.

Crash Nitro Kart
In this game, there are four colored gems: blue, red, green, and purple. Each of these gems is acquired by winning the corresponding gem cup. The gem cups are unlocked by obtained all CNK tokens of the same color. Obtaining all give colored gems unlocks Hyper Spaceway in adventure mode.

Crash Twinsanity
In this game, there are only colored gems, and clear is considered a color. A lot of them are hidden, and there are six of them in each hub/level.

Trivia

 * Spyro also has a usage for gems, like Crash has a usage for Wumpa Fruits.