I cut in half, roast and scoop as a first choice, but if I need uncooked, diced squash, I dice it with the skin on, and then cut the skin off the individual pieces of diced squash with a small paring knife. It might be touch more time consuming, but its so easy to just slice off a little patch of skin as opposed to struggling with a big, heavy squash.

'My veggie peeler works magic everytime

Supposedly, if your knives are very, very sharp, peeling a squash is as easy as slicing cake. Hah! Not.

Use a metal skewer or an ice pick or a long nail to poke four holes through the squash and into the seed cavity. Put the whole squash in the microwave. Nuke on full power for a minute for a small squash or up to three minutes for a large squash. Or, put the whole squash in a very large pot, fill it with enough water to cover, bring to a boil, shut the heat off and let the squash sit for five minutes. Either method allows you to easily peel the squash but still have raw squash to slice and dice any way you want.

I just picked my last Blue Hubbard. It's too big for the microwave and any pot I own, so I'll probably cut it in half and boil for a few minutes it cut side up in a roasting pan.

About the only time I peel first is when I want to dice and roast; when I do that, I cut the long, skinny neck off from the rounded portion, giving me a couple of flat surfaces; stand it on the cutting board on those flat ends, and use my chef's knife to hack off long, straight peels. It's a pain, but it works.

I like to roast slices of butternut squash (and this past week had a lot of practice). I use a regular potato peeler and peel the squash. Then I hold the squash with a little cloth hand towel by the long end and start slicing the bulb end first. That makes it very easy when you get to the long part of the squash. Then I trim the seeds out of the slices. The seeds are great to toast with a little sea salt.

Until recently, I only roasted, halved lengthwise and cut-side down. I do find, however, that you can get some really nice caramelization when you dice and then roast. (For example, by Autumn Vegetable Hash can only be made by peeling and cutting before cooking the squash.) I'm with pierino. I cut lengthwise, then quarter, then, standing each piece upright on the cutting board, with the peel on the right side (as I'm right handed), use a cleaver for long, straight cuts, followed by a good sharp peeler to get the rest. (I dream of cooking with a cleaver and a pair of chopsticks as my only tools. . . . ). It actually doesn't take that long. I don't peel acorn squash. Period.

Is there a reason you need to take the skin off first? If not then bake and yank it off after it's roasted, per previous answers. If you do need to take it off, forget the peeler and go with a chef's knife or chinese cleaver. Split the squashy wash first though, so that it will be stable on a board when you hack away it. There will be some waste, but then it's a mean old world.

I like the skin...even of acorn squash. But I may be unique in that.

For butternut - I often poke a couple holes in them and then microwave for one minute - seems to lossen the skin a bit. Also a serrated peeler makes a huge difference.

Go with roast and scoop method. It works better and is much, much easier to accomplish.

Acorn squash is a pain to peel because of the shape of the ridges. I find it easier to cut in half, then roast, then scoop out. That makes it difficult to use as chunks in a salad or something, but the flavor is so mild that I usually puree it for soups or baking, anyway.
Butternut squash, though, doesn't cause me trouble: I just use a vegetable peeler. (specifically this one: http://www.simplygoodstuff.com/star_peeler.html though anything with a good enough blade should do the trick.)