This is a very broad question and the answer pretty much is "all types of trout flies." However, the replies above are good ones. Trout flies are usually categorized as one of the following types: dry flies, wet flies, nymphs, and streamers. The flies described in this thread are mostly specific flies known as "patterns." These patterns, in turn, are categorized by size and this refers to the hook size - for example, a "#14 Hare's Ear" refers to a medium sized fly (#14) from the nymph category. When shopping for flies, if you tell the fly shop the name of the fly and the size they can usually get you that specific fly.
Here in PA, most fishing for stocked trout is done in the springtime for fish that have been stocked recently (this would mean within a month or less). For these fish under the typical conditions, a basic box with a dozen or two flies of the varieties described above will cover most bases.