Final Fantasy VII/Things to Collect

Materia caves

HP <-> MP: Found in the cave north of North Corel (the ropeway station). You must have a river chocobo to reach it.
Quadra Magic: Found on an island to the east of Chocobo Billy's Farm. You must have a black chocobo to reach it.
Mime: Found on Wutai Island, on the eastern edge south of Wutai's northern peninsula. You must have a mountain chocobo to reach it.
Knights of Round: Found on Circle Island, an uncharted island in the northeast part of the world map. You must have a gold chocobo to reach it.

Turtle's Paradise flyers

Throughout the game, you will find posters that advertise Turtle's Paradise, the restaurant in Wutai.

Sector 5 slums - In the top floor of one of the houses.
Shin-Ra headquarters, first floor - on the bulletin board. (You have to read this on either time you're visiting the building, or you'll miss it for good.)
Gold Saucer - Ghost Square shop.
Cosmo Canyon - Weapon shop.
Cosmo Canyon - Shildra Inn.
Yuffie's House in Wutai - In the cellar. (You need to read this when Yuffie takes you in there, or you'll miss it for good.)
After viewing all the Turtle's Paradise flyers, you have to read the main poster in front of the Turtle's Paradise bar in Wutai.

If you find them all, you can collect the prize from the barkeeper in Turtle's Paradise.

Ribbons

Ribbons are the most handy accessory ever devised by a FF designer. They're also pretty rare. Here are some places to get Ribbons, though:

A chest in Temple of the Ancients.
Master Tonberrys can be morphed into extra Ribbons.
There's a pretty well-hidden cave in Gaea's Cliff.
Special Battle in Gold Saucer, though they are reportedly pretty rare.

Bone Village

The Key to Sector 5 can be found by looking for normal treasure. If the tremors point toward fighter plane's nose on the lower plateau, dig just under the tip to reveal it. This is the most probable location for it, though it may reportedly vary.

Lucrecia's Waterfall

You need a colored chocobo or a submarine to reach the round lake on the southern half of the western continent. There's a cave behind the waterfall.

Once you enter with Vincent in your party, you get a cutscene that explains a lot about Vincent's background. (In Disc 2)

Return to the cave after about one hour or more of play time (in Disc 3). Doing so, you'll get Vincent's level 4 Limit Break manual (Chaos), and Vincent's ultimate weapon (Death Penalty).

Sunken Gelnika

A big airplane has sunk in front of Costa del Sol. Use the submarine to reach it.

Inside, there's first a save point and a chest. In the second room to the left, not up the ladder, you have to fight Rude and Reno of the Turks. Rude does Bolt2, and both Reno and Rude both have admirable physical attacks that will amp your limit bars. Two good strategies here are to equip Steal materia and steal the most invaluable and prized armour in the game, Ziedrich from Rude, and to use Hypers on your party to quicken their wait time and fill their limit bars faster. This is one of two chances to steal the Ziedrich armour from Rude, so you can have up to two!

The third room is the cargo room. Behind the pipes, you'll find Hades materia. In the chests, you find Conformer, Yuffie's ultimate weapon, Highwind, Cid's lv4 limit break manual, and... other stuff?

The enemies here are very strong, but they can be morphed into Sources, which raises your stats. Getting Sources here is the only way to raise stats to the max value of 255; you cannot reach this point by leveling up.