I've been reading up on this a bit recently as there is a lobster research lab across the hall from my own lab. First off I was surprised to find that you can train lobsters to do tricks. You can train them to turn in a circle, to flip over on their backs, etc. - simple stuff but far more indicative of complex nervous system than I had assumed. One trainer I know who worked with a particular lobster for a long time swears that he was doing pretty well on a "match the shapes" training task, which is considered fairly advanced behavior. Their social behavior is also now known to be pretty complex. This all adds up to a more complicated central nervous system than they had been given credit for. As for pain specifically, there are over a dozen studies now - bear in mind nobody had really studied this at all till Elwood got into it about 8 years ago, and his lab's churning out papers now, and a couple of other labs are now on it too. The most consistent clues regarding pain are: crustaceans show strong avoidance responses to tissue damage, they show characteristic confusion/nonsheltering/other abnormal behaviors after severe damage to a body part exactly as vertebates due, they immediately begin repetitive grooming of the injured body parts (analogous to a vertebrate licking an injury site), and they clearly remember and avoid things that caused tissue damage in the past (in vertebrates, that type of learning is considered evidence of experience of pain). They also have nociceptors (sensory neurons that appear designed to detect tissue damage and that are connected to the central nervous system. Most intriguingly, application of local anesthetics decreases all the above responses.

Put those all together and it starts to sound like they do experience pain. It's never going to possible to prove what their subjective experience is, but the necessary wiring is there, the behavioral responses are appropriate, and from an evolutionary point of view it would make sense for long-lived animals such as these to evolve the ability to sense pain. (Lobsters live many years.)

I have no problem with eating animals as long as they don't suffer. But now I think lobsters shouldn't be boiled alive, unless we can prove they do NOT feel pain. That is, I think the burden of proof should be in the other direction.

PS - some more sources - source, source, source, source, a decent review, and finally Elwood's most recent 2012 review. Personally I think he makes a pretty good case. YMMV