We received some terrific tips in the comments yesterday. I have compiled them here for one anyone who'd like to print them out. And as always, and especially for the non-short story scribes in the crowd, there's coffee, tea, and lounge chairs in the Comments. . .
From paul lamb: I've found a lot of engines that will cough up markets. Duotrope's Digest is a good one. Neatly and sensibly organized. Updated regularly.
From farfetched: Asimov's takes new author submissions as well for sci-fi. He also says: there's always the online route — it's a way to get your stuff out in front of an audience, and it has worked for several people (example: Scott Sigler).
From conda: Ralan.com is an excellent listing of short story markets. And for mysteries, the yahoo group Short Mystery Fiction Society is good. She adds: a newsletter called The Gila Queen's Guide to markets. You have to pay for this one, but it's dirt cheap for everything you get, pages and pages of market and publishing info, including occasionally an anthology that is open to newbies.
From usiku: writers could get together and use their individual and collective networks to publish and market their own book of The Best Neglected Short Stories or magazine of the same.
Guy Hogan has a blog with flash fiction tips.
Updated: I removed one of the original recommendations. I'll investigate a bit more. If it checks out, I'll put it back up.