> Geneon, ADV, Sentai, Discotek/Eastern Star, Animeigo, Funimation, Viz, NIS, Aniplex
> of America, Mediablasters, Manga Ent, Nozomi/Lucky Penny, GKids.
To add to this list (most of these companies are also defunct):
Pioneer, Bandai, RightStuf, Central Park Media, US Manga Corps, Tokyopop, Synch-Point, Honneamise, Pony Canyon, Software Sculptors, Anime Works, plus a few others I'm sure I'm forgetting. Some of the ones I've mentioned are just prior names of other companies mentioned above.
If dealing with hentai/yaoi, there are other names to deal with, though to be honest, I don't see those bootlegged nearly as often. The big names here are Kitty, Critical Mass, Anime 18, and Adult Source Media.
Now, names to avoid. These are known bootleg companies:
Anime Cartoon, Anime Studio, DVD Ani, fx, Manga Cartoon, Manga International. (Don't confuse those last 2 with Manga Entertainment, a legit company most known for Ghost in the Shell.) This list is also not complete, but is just most of the names I recall having seen.
The only hard and fast rule I can think of for identifying a bootleg DVD is the episode count. I can not think of a legit DVD with more than 7 full-length episodes on it. Anything advertising 24-26 episodes on 3 disks is bootleg. Other common warning signs (but NOT guarantees) are disks with ALL region (CPM released quite a few of these), or sets in a cardboard foldout. Almost all bootleg sets have these properties, but there are legit releases with them also. (If it helps, I can't think of any legit cardboard foldout that is also all region, though I won't say there can't be one.)
Lastly, for non-US releases, the only real change is the list of legit companies. I won't go into that, since you're unlikely to see them. If you have a question about any release, check Wikipedia for the title. Older companies may require reading the page as opposed to checking the quick fact bar. (Slayers, for instance, states the current license holder, FUNimation, but you have to read the article for the CPM mention.)