I currently have them in ziploc bags, but I'd like to have a system that keeps them organized and quickly accessible in game. What have other people used?
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If they are not too thick you could try accordion folders. That way you can separate them by type (muddy, rocky, crypt... whatever).
I currently use a number of boxes reclaimed from boardgame expansions that didn't need them; I have the tiles sorted somewhat into wildnerness, dungeon, city, and so on. Each box has a ziplock bag to contain the little tile bits (i.e. dressing, and small-size tiles). It's not optimal, but it keeps them tidy when put away.