Seems like every non-entomologist I know in Tucson (including my husband) thinks these flies are bees and totally lose their minds when they end up indoors:
Giant bee-mimic fly in my house! That's Copestylum isabellina, according to the fine folks at BugGuide.net
I have seen a number of otherwise calm, rational people completely panic and either a) start running around hysterically (sometimes screaming a bit) because one of these flies was “chasing them” or b) curl up into the fetal position, apparently hoping that they will spontaneously achieve telepathy and convince the fly to leave. Attention all Tucsonans: it’s a harmless fly! If you don’t know how to tell the difference, check out my Monday post for the things to look for to be sure.
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The Dragonfly Woman 
There are many species of flies that mimic bees; from an evolutionary standpoint, that can give them extra protection, as people or animals are less likely to mess with something that might sting them. Some bee flies (that’s what they’re called) look less bee-y and less threatening than others:
http://portraitsofwildflowers.wordpress.com/2011/07/31/a-pretty-fly/
Yeah, there are tons of different flies in the world and they are a super diverse group. My favorite of the bee mimics are the Bombyliidae (especially those in the tribe Bombyliini) because they are all fuzzy and adorable, although I think many of the Syrphidae (like the one in the photo) are more convincing mimics.