There are hundreds of ways to eat
1) Baked maple squash. This is best with smaller varieties like acorn or delicata. Cut in half, scoop out the seeds and pulp from both halves, and place cut-side up in a baking dish with just enough water to cover the bottom. Mist with olive oil and sprinkle lightly with salt. Drizzle a tablespoon of maple syrup in the middle of each half, and bake for an hour at 400 degrees. Simply Recipes shows you how good it will look.
2) Curried coconut squash soup. The hardest part of this endeavor is simply cutting a sizable squash in half (we used a 3 pound Blue Hubbard) without breaking your best kitchen knife. (Try chiseling, rather than sawing, to crack the rind.) Prepare and bake as above, minus the maple, for about 1 1/2 hours or until very tender. While the squash cools down enough to handle, sautee some diced scallions and/or onions with a few pats of butter in the bottom of a large stockpot for 5 minutes. Add 1/2 cup of dry white wine, 2 tablespoons fresh grated ginger and 1 tablespoon curry powder (or garam masala, chili paste, whatever you like), and cook until wine is nearly evaporated. Use a metal spoon to scoop out the flesh of the squash into the pot, along with 4 cups of water, 1 cup of coconut milk, and a sprig of fresh thyme (or 1 tsp dried). Simmer for 15 minutes, then puree with a hand blender until smooth. Add more water or coconut milk to adjust texture; sprinkle in some salt and play around with other spices until it tastes perfect! There's a more precise recipe on Food52.
3) Squashed squash. You can substitute squash for potatoes in a mashed potato recipe, or combine the two vegetables, as in this Bon Appetit recipe. For a sweet version, follow the baked maple squash recipe and simply scoop it out of its shell at the end. Smooth out the lumps using an electric mixer, hand blender, or even just a fork. Eating Well has a recipe for Mashed Maple Squash.
4) Squash risotto. I love this Moosewood Cookbook recipe, which mixes kale and chunks of winter squash into a basic white-wine risotto. It's easier than I expected---although you do have to be vigilant about stirring!---and it's a very healthy dish, yet the creamy arborio rice makes it taste decadent.
5) Stuffed squash. I like chopped apples and cinnamon-spiced couscous inside baked squash, and this inventive recipe for " quinoa stuffed sweet dumpling squash" looks so good that I'm already counting it among my favorites. (Carnivores might prefer Alton Brown's stuffed squash with pork and rice or Rachael Ray's stuffed acorn squash with beef and couscous.)