Love Maine! Lot of great recommendations already in this thread. Just to add my two cents:
Visit the wild places. Lots of moose and bears to be seen if you spend some time in the state or national parks. Baxter State Park as suggested is amazing. I saw moose and a black bear when visiting it. If you like golf, Samoset Resort on the coast is amazing and calls itself something like "the pebble beach of the Atlantic." Otherwise, Belgrade Lakes was a fun course with lots of elevation change. Dining on lobster rolls or other local fare seems to be a great bet. When I was there my favorite was the "The Porthole" in Portland. I think it's been in existence forever if memory serves correctly.
I taught golf for a summer in Maine and enjoyed my experience tremendously. Thus, my experience was only in the summer, and not the other seasons, but I'd recommend those places above, and those were my best memories.
Edit: if you want to be a real "Mainiac" try Moxie soda. Come back and let me know what you think;-) Bleh! LOL.