Support materia just helps your magic or other random materia around. You really have to test out each blue materia to see what they do. Here you will see the list of support materia from the game and my rather random descriptions of them, including which kinds of materia can they connect to andhow much AP you need to be able to get to the next level of the materia. (what? levels? yes, materia does grow, you know).

There really is no drawback to to equipping support materia except that some of the support materia seem to do little use to you or you just simply don't have enough room to equip it on...miraculously.

One good thing is that you can sell Mastered All materia for 1.4 million gil ^^.

NAME OF MATERIA	WHICH MATERIA IT CONNECTS TO	HOW MUCH AP YOU NEED...	DESCRIPTION
All	Magic (green)	* - none * * - 1500 AP * * * - 6000 AP * * * * - 18000 AP Master - 35000 AP	What this does is that it makes most magic and when cast, it casts on every enemy or every character, depending on which magic. It's pretty cool and VERY useful.
Elemental	Magic (green) Some summon (red)	* - none * * - 10000 AP * * * - 40000 AP Master - 80000 AP	I find this pretty useless. What it does is that it carries that particular magic status on the weapon or lets you get protection on the armor.
Added Effect	Magic (green) Summon (red)	* - none Master - 100000 AP	Yet another useless materia. Linked on your weapon w/ a magic, it will get that condition if it its (works with status materia). Linked on your armor, it protects you.
HP Absorb	Magic (green) Summon (red) Command (yellow)	* - none Master - 100000 AP	When connected to the source materia, your character will have their HP filled up by 1/10 of the amount of damage given....
MP Absorb	Magic (green) Summon (red) Command (yellow)	* - none Master - 100000 AP	It's the same as the above except this time it's 1/10 of your MP ^^.
Added Steal	Magic (green) Summon (red) Command (yellow)	* - none Master - 200000 AP	Attached to whatever materia used, it'll have the character attempt to steal an item from the enemy. Doesn't work on some command materia, though....
MP Turbo	Magic (green) Summon (red)	* - none * * - 10000 AP * * * - 30000 AP * * * * - 60000 AP Master - 120000 AP	This is soooo useless! Even I don't even know what it does!
Sneak Attack	Magic (green) Summon (red) Command (yellow)	* - none * * - 20000 AP * * * - 60000 AP * * * * - 100000 AP Master - 150000 AP	For any battle that begins, the materia linked to this materia will automatically cast the spell. It only happens a certain percentage and gains percent level as the materia levels up.
Added Cut	Magic (green) Summon (red) Command (yellow)	* - none Master - 200000 AP	This is my second fav. support materia. Hook it up to Deathblow, and hahahaha.....
Magic Counter	Magic (green) Summon (red)	* - none * * - 40000 AP * * * - 80000 AP * * * * - 120000 AP Master - 200000 AP	I never used this materia, either, so I really can't tell you what it does. Probably some other useless thing that can only be good when it's mastered.
Final Attack	Magic (green) Summon (red) Command (yellow)	* - none * * - 20000 AP * * * - 40000 AP * * * * - 80000 AP Master - 160000 AP	This is another good materia when you hook it up with Phoenix. Whenever the possessor of this dies, he/she will automatically cast a spell at its highest level. Its use will increase as the materia increases.
Quadra Magic	Magic (green)	* - none * * - 40000 AP * * * - 80000 AP * * * * - 120000 AP Master - 200000 AP	This is my favorite support materia. Hook it up to a magic materia, and then it'll cast the spell four times. Imagine casting Flare four times at your enemies!
Command Counter	Command (yellow)	* - none * * - 40000 AP * * * - 80000 AP * * * * - 120000 AP Master - 200000 AP	This can only be used with Steal, Sense, Throw, Morph, Deathblow, Manipulate, and Mimic. What it does is that it'll automatically activate itself when something happens to the person equipped with it. It's only found in the final dungeon, though, so what's the use of having it?