My advice is to go to xivdb.com and look up whatever you have and see what it crafts into. If you intend on making all items at some point, at least that site will let you know how many you need. When I was mining raw stones like spinels, goshenites, zircon, etc, ffxivdb was able to show me how many I would need to craft every item they can be used in, so that's how many I kept, and I sold the rest. Also, have a look on the marketboards. If you are hoarding NQ chocobo feathers, don't bother, as they are probably dirt cheap- any level 25+ gathering mat is probably in this same category due to the number it takes to level as a gatherer. Logs are the same way. Why keep them when you can buy 99 for like 900 gil?

Someone mentioned only keeping raw base materials though, which I disagree with- if you only keep the raws, you will need to craft them into intermediate materials (ingots, lumbers, etc) which all uses many SHARDS- which become the crafting bottleneck at about level 35. You WILL run out, and have to buy them, and RMT are pretty much controlling the market, so you will not get them cheap. Why waste them if you don't have to. Example, Mythril Ingot is 3 ores + 4 wind or fire shards. Cost to craft an ingot, roughly 200 gil. Price to buy one can be as low as 120 depending on how many are for sale. Don't craft these unless you are trying to HQ them for other crafts, or you are leveling on them.