This one's been coming up a lot lately on area list-servs, message boards, and other genealogy resources. People run into Middle Haddam, Haddam, and East Haddam and treat them like they're the same town. Since this runs straight into what I'm researching right now, I thought I'd clarify.
1) Middle Haddam is not a town. It's a village of East Hampton. And it has nothing to do with the other two Haddams. Middle Haddam, as part of East Hampton, was originally part of Chatham, and before that, East Middletown. Recent records will be held in East Hampton. Historic records may be in Portland or Middletown.
2) Haddam is due south of Middletown on both sides of the Connecticut River. (This was news to me! Haddam Neck - part of Haddam - is one side of the river, while Haddam Center and Higganum are on the other side.) Founded in the 1660s, it originally held East Haddam, which is across the Connecticut from Middletown. Haddam was originally one of Middlesex County's two county seats.
3) East Haddam began as part of Haddam but gained its independence in 1734. The area's first church was founded in 1704, so you should be able to find local records very early on.
Check out the linked sites for more information on the history of each village and town. Happy research!