Although I am not an authority on Chinese dumplings, I do like them. So for the past several weeks I've been making occasional trips to restaurants reputed to serve good ones. Most have probably been mentioned here, but I don't recall for sure.
My favorite is Luscious Dumplings (704 W Las Tunas Dr, San Gabriel, 626 282 8695). It's an unpretentious little place in an unpretentious little strip mall on Las Tunas Dr, which LA Weekly listed in its "best streets in LA" (or something like that) for its low-key vibe and old (for LA) architecture. The great revelation at Luscious Dumplings, aside from general freshness and overall quality, are the "soup" dumplings. They're dumplings that have pork or whatever inside, but that also have soup inside, so that when you bite them you get a blast of warm flavorful soup in your mouth. It's quite strange and wonderful. (This was definitely mentioned in a message on Chowhounds.)
Next favorite are the plain old potstickers at Yang Chow in Chinatown (no address handy, sorry). They're just excellent, cut-above potstickers, with lots of meat and a wrapping that's much thicker than usual and just rubbery enough to be good without being, uh, rubbery. Yang Chow also has two things that are crucial to my own enjoyment of Chinese dumplings: high-quality chili paste (a slurry of crushed red chilis in oil rather than the nasty stuff in plastic bottles, or worse, that some places have) and fresh ginger. I haven't actually been to Yang Chow for some time -- I hope it's still there.
The biggest disappointment is Din Tai Fung (1108 S Baldwin Ave, Arcadia, 626 574 7068). This is a moderately large dumpling place that's packed on weekends. I went there this morning at maybe 11am, for example, and got a table after only a twenty minute wait; if I had arrived at noon then the wait would have been forever. The first time I went to Din Tai Fung, the wait actually was forever, so I went to the inside desk and ordered take-out. (They have these order forms you fill out on little clipboards.) I got the dumplings and drove to the LA Arboretum which is nearby. (If you're coming from most anywhere, you'll get to Din Tai Fung via 210, the Baldwin exit south, and you will pass the Arboretum on your right, then you'll pass a large shopping mall on your left, and then Din Tai Fung will be on your left.) I ate the dumplings there at the Arboretum, and something was wrong with them. They tasted distinctly undercooked, and the fillings were grainy and uniformly tasteless. After a while I realized -- oh, stupid me -- the take-out dumplings were meant to be taken home and steamed! Feeling sheepish, I made another trip back there (i.e., this morning) and got an actual table. But the dumplings tasted just the same -- undercooked. Not everything was bad. Their buns were quite good, unusually soft and fresh, and they had some unusual sticky-rice things. But the dumplings were -- I dunno, like I was completely missing the boat or something. And their ginger was tasteless too, and their chili paste wasn't that great either.
Finally, Dumpling Master (423 N Atlantic Blvd, Monterey Park, 626 458 8689, very close to the Ocean Star dim sum empire). I went there late one evening for a snack and everything was crummy -- the attitude, the interior of the restaurant, bleah. I can't actually recall why I didn't like the dumplings, but I sure didn't like them. It was one of those "maybe they made these so bad on purpose because they don't like white people" moments that I'm always embarrassed about, while still being annoyed and disappointed. Who knows, maybe I got the wrong thing or went at the wrong time or something. I'm open to being enlightened by those with greater knowledge.
Anyway, that is my survey of Chinese dumplings. If anyone knows of superlative Chinese dumplings elsewhere, do let me know.