FamilySearch has collection pages for town records from Massachusetts, Vermont and New Hampshire, but not from Maine. Nevertheless, images of the records from many Maine towns are in fact available on FamilySearch, if you know where to look.
Start with the FamilySearch Catalog. Enter a town name and FamilySearch will change it to a standardized version.
Clicking on the "Vital records, 1800-1891" link brings us to the catalog entry page. Scroll to the bottom to find the "Film Notes" section. This tells us whether the resource can be searched (magnifying glass), can be viewed online (camera), or is available on microfilm (film reel).
Clicking on the camera brings us to the Film Viewer. If you're lucky, there will be an index at the beginning or end of each volume. If not, you'll have to page through each book to find the records you need. In this case, I'm looking for the birth record of my great-great-grandfather Lemuel Dunham. I see from the index that it should be on page 140. After a few moments browsing, I find the record I'm looking for.
Some towns have records online, others do not. In some cases, the catalog says that images are available, but an error message appears when you try to view them. If the town records you need aren't yet available, check back later, as presumably more images will be uploaded in the future.