How do i know how many skins i have?

I was recommended the LolSkinView app. You log in and it takes inventory, and it'll show you prices and other information alongside a list of what you do and don't own (may not be working with the new client). Pretty sure there are some sites that'll do this too, though I don't know any off the top of my head.

Not from Riot, although many people have suggested and asked for a skins tab.