In general, fly reels are pretty tough. Can't say I've ever actually broken one by dropping it. The most frequent case for me is I slip, and realize I'm going down, and the rod gets tossed to free up my hand to catch myself. I think I've done more damage to my wrist, than my reels, by doing this.
One time on an el cheapo Cabelas house line reel I bent the rim of the spool a little doing this. Just bent it back out with pliers so it would clear the reel housing and not rub. Had some cosmetic blemishes as a result, but it still worked fine after that. (I tend to think fly reels look cooler once they're scuffed up a bit anyway.)
Other than that, the mechanical issues I've had in response to dropping reels have all been from getting fine gravel or sand in them, as others have mentioned. This causes the spool to not spin freely sometimes. This can also sometimes happen inadvertently just setting your rod down to unhook a fish...Try to avoid setting the reel in sandy areas when you can. When this happens on the stream, I usually just take the spool off and rinse everything good in the water, put it back together, and keep fishing. Fly reels (as opposed to spinning reels) usually deal with getting their internals wet pretty well. They don't usually bind up when you get them wet. (Though I try to avoid it, I know many guys just freely dunk them in the water when letting a fish off.) If I ever dunk the reel, when I get home I just take the spool off and let it sit open and dry on my work bench for a few days before putting it away.