Independent materia is just as what it says. It's independent. You can't junction it with anything: it acts on its own. However, most of the independent materia is pretty useful to HELP you.

Others are a bit useless and can be hard to get in all of the Gold Saucer games. Some are totally weird because you pretty much have no use for them and wonder why the creators put these certain independent materia in there. *sigh* Oh well.

There really are no drawbacks to using independent materia. Really, use them to your hearts extent and how many slots allow it.

NAME OF MATERIA	HOW MUCH IT COSTS	HOW MUCH AP NEEDED...	DESCRIPTION
Cover	Buy - 1000 Gil Sell at Master - 70000 Gil	* - none * * - 2000 AP * * * - 10000 AP * * * * - 25000 AP Master - 40000 AP	Um...basically, whoever has this equipped, will jump in front of a character about to get hit like a guard and takes the damage. Odds of it happening depends on what level you're on.
Counter Attack	Win at the Gold Saucer chocobo races Sell at Master - 1 gil	* - none * * - 10000 AP * * * - 20000 AP * * * * - 50000 AP Master - 100000 AP	This is one of the better independent materias ^^. Depending on the materia's level, your character will counter attack automatically after they're hit.
Long Range	Find in the Mythril Mines Sell at Master - 1 gil	* - none Master - 80000 AP	With this thing equipped, your character who usually attacks short range can attack enemies that are far from their reach.
MP Plus	Buy - 8000 Gil Sell at Master - 56000 Gil	* - none * * - 10000 AP * * * - 20000 AP * * * * - 30000 AP Master - 50000 AP	As you gain levels on this materia, your max MP output is increased. It's pretty cool if you ask me ^^. This also depends on how many MP Plusses you have equipped on you. A must to equip once you get the chance to buy.
HP Plus	Buy - 8000 Gil Sell at Master - 56000 Gil	* - none * * - 10000 AP * * * - 20000 AP * * * * - 30000 AP Master - 50000 AP	This is similar to MP Plus except that it increases your max HP output. Once again, a must to equip and buy once you have the chance.
Luck Plus	Find this at the Temple of the Ancients Sell at Master - 1050000 Gil	* - none * * - 15000 AP * * * - 30000 AP * * * * - 60000 AP Master - 100000 AP	Depending on what the materia's level is, your character's luck is raised. Personally, I found no use to this ^^. I just wanted to sell it.
Magic Plus	Find this in Zango Valley Sell at Master - 1400000 Gil	* - none * * - 10000 AP * * * - 20000 AP * * * * - 30000 AP Master - 50000 AP	Your equipped character's magic power increases depending on the materia's level. Another no use for this. I just sold it for a lot of mula ^^.
Speed Plus	Win this at the Battle Square in Gold Saucer - 12800 BP in Disc 1, 4000 BP in Disc 2 Sell at Master - 1400000 Gil	* - none * * - 15000 AP * * * - 30000 AP * * * * - 60000 AP Master - 100000 AP	Similar to the last two, depending on your materia's level, your character's speed will increase by certain percentages. I never really used this since I had too little space to equip it.
Chocobo Lure	Buy - 2000 Gil Sell at Master - 1 gil	* - none * * - 3000 AP * * * - 10000 AP Master - 30000 AP	This is a must if you wanna go chocobo breeding or just to get to the Mythril Mines in Disc one. Running around the Chocobo tracks in various places, the level of materia depends on how often you'll encounter chocobos in battle.
Gil Up	Bought at Gold Saucer's Wonder Square - 1000 GP Sell - 1 gil	* - none * * - 80000 AP Master - 150000 AP	I never got this, so I don't know what it does ^^;;;
XP Up	Bought at Gold Saucer's Wonder Square - 2000 GP Sell - 1 gil	* - none * * - 60000 AP Master - 150000 AP	See the above.
Pre-Emptive	Bought at Gold Saucer's Battle Square - 6400 BP (disc 1), 1000 BP (disc 2) Sell at Master - 1 gil	* - none * * - 8000 AP * * * - 20000 AP * * * * - 40000 AP Master - 80000 AP	Basically, what this does is that you get the chance to attack first during battle (meaning that your enemies have their backs turned). Your chances of having this depends on the level of this materia.
Enemy Lure	Bought at Gold Saucer's Batte Square - 800 BP (disc 1), 250 BP (disc 2) Sell at Master - 1 gil	* - none * * - 8000 AP Master - 20000 AP	Once you get at level 2 of your materia, you have a 100% chance of running into enemies no matter what (that's 2x the normal amount you usually run into ^^)
Enemy Away	Win at Chocobo racing Sell at Master - 1 gil	* - none * * - 8000 AP Master - 20000 AP	This is the opposite of Enemy Lure. You have a 75% chance of NOT running into enemies when this is at level 2. Why would you want to get this anyhoo? Wimp!!
HP/MP Switch	Only able to get this when chocobo breeding; get a river/mountain chocobo and go to North Corel materia cave Sell at Master - 1 gil	* - none Master - 80000 AP	This materia is pretty pointless. I mean, why would you want to switch your MP max to your HP max for?
Super Enemy All	Found in Final Dungeon Sell at Master - 1 gil	* - none * * - 10000 AP * * * - 20000 AP * * * * - 50000 AP Master - 100000 AP	This is really cool ^^. Instead of the normal "attack" you have "slash all" in place of it. Steal, Sense, Morph, Deathblow, and Manipulate can be used with this. How effective it is depends on how high the level is.