jlevine, some of the answer to "when is the best time to dive in Thailand" depends on what you are looking for. The consensus is that the very best diving we have to offer is in the Andaman via liveaboard to the Similans and Surins national parks, which include the islands themselves and the surrounding seas. So if that's what you're aiming at, you need to think about conditions on the west coast of the country.
As others have said, on the west coast we have generally great conditions between November and May, but as Buadhai says, there is some variation from one year to the next and it's best to check updated weather pattern maps to know what to expect. That doesn't help you plan, though, does it? What I generally tell people is that weather can still be changeable in the months of November and April, simply because we never really know ahead of time exactly when the winds will shift from the southwest monsoon (our wet season) to the northeast monsoon (our dry season). Some years we get perfectly dry and calm Novembers and in other years the entire month is still unsettled weatherwise. The same is true for April. So if you are looking for flat water, your best bet is sometime from December to April. If you want the clearest water, come earlier in the dry season. If you want the best chance for big pelagics like manta rays, come later in the season when the plankton levels are more pronounced. Mid-December to mid-January tend to see a lot of visiting Europeans (when the economy isn't keeping them home). Most of my American customers seem to come in November or February/March.