I wholeheartedly agree with the Bintliff's recommendation. They serve brunch on Saturday and Sunday during the winter - 8am to 2:30pm. The food is extremely creative and excellent. When we go there with friends, we tend to order lots of different things and share (FYI, you can order one pancake or french toast instead of a whole order). I highly recommend the creme brulee french toast, chocolate chip macadamia nut pancakes (no syrup needed!), crab cake benedict (the hollandaise sauce is the best) and the corned beef hash. I recommend their spicy Bloody Mary, too, and I'm not usually a Bloody Mary drinker.
The interior design of the restaurant is also worth mentioning - very quaint (lace curtains, dried flowers, etc.).
For a great brunch menu check out Bintliffs right on Route one. They have an extensive, delicious menu including 5-6 different varieties of pancakes, waffles, omelets, as well as sandwiches, etc. The food is delicious & different than your run of the mill Breakfast place.
I am not positive about what is open- many places are not open (Amore, Egg and I, Omelette Factory). For brunch on Sunday MC Perkins Cove- in P. Cove- has a really good brunch with jazz on Sunday but they may be on vacation for a few weeks at this time.. Also, you might try the Old Village Inn in the Center of Town. They are usually open all winter. If the Village Market is open ( they close for a few weeks in winter- not sure when) - it is in Ogunquit Center- they have lots of breakfast choices.
For Saturday- drive back down Route 1 to York- heading south, a couple of blocks past Stonewall Kitchen on the left is a place tucked behind a credit union- called "Food and Co" that has a very good breakfast. Stonewall Kitchen in York on Route 1 has a great cafe- call them to find out if they are open for breakfast.
Bessie's in Ogunquit Center is open year round. Have never been but there is a place called Raspberri's in the Gorge Grant Hotel in Ogunquit (Rte 1) that advertises as open year round and has "famous belgian waffles".
Generally, Og is pretty dead this time of year. Hope you have fun!
One place that will be open for sure but a bit of a drive north on Route 1 is the Maine Diner.