Same here. It works only sometimes. Tried on Yamaha receiver, direct to optoma projector and to Vizio 42" TV direct. The only incantation that ever worked was plugging into the Yamaha and turning on *both* the projector and the TV (the yamaha can do both simultaneously). Another clue is: regardless of output, the yamaha receiver lights with a red HDMI when it detects the iPad2. That seldom lights (it does on the rare occasions that it's all worked).
Given that hdmi is a serial bit transfer technology with some pretty complex handshaking to handle sound, various resolutions etc. I suspect that Apple either has a problem in the adapter (likely) or the iPad2 software (possible but since it works with VGA and standard video, unlikely). HDMI, however, is well defined and testing is easy. Since so many various manufactures and devices work fine and robust with HDMI, it's clear that this is an Apple iPad2 problem, and it seems that Apple is not going to fix it on the iPad2...period...ever.
Apple has a lot of smart engineers and I'm confident they've investigated this and know the problem. (Engineers have a lot of capable test equipment). Whatever the problem (adapter, software, connectors), Apple can't really say because as soon as they admit the problem (and fix), then the 10 million iPads come screaming back and sales fall off. So even with a diagnosis and/or fix, they keep silent. Bad service, good business. For now, I'm taking all of these 5 pages of posts as "the HDMI for iPad2 simply doesn't really work, well not in any reliable, useful sense".
Their customers have spent ENOUGH time diagnosing this bug of Apple's. It's a failure of the iPad2 and thus simply part of its (revised) spec. Otherwise a capable machine and worth it even without HDMI. If HDMI is required, iPad2 is the wrong product.
If keynote is required, use VGA... more commonly available anyway, as you travel.
