I wear goggles when downhill skiing except in very mild conditions. For one thing, my eyes water too much otherwise.
However, I did go through the whole prescription sunglasses thing for cycling and nordic skiing. (Tried contacts and couldn't make them work for a variety of reasons, primarily that I just could not get the crisp distance vision focus that glasses give me.) I'll wear them for alpine, too, on a spring bump day or similar.
Anyway I ended up going with Oakley Half Jackets. I've had them for a couple of years. They're all plastic and rubber, partially addressing alexzn's point about safety above. This choice has worked out well. I'm not brand loyal, and am not saying that Oakleys are "better" than any particular other brand; just reporting my specific experience with the glasses. (My experience with Oakley as a company is slightly less clearcut, as you'll see if you read on.) The optical clarity seems excellent, notwithstanding a few scratches that are more or less inevitable if you mountain bike, as I do. The best decision I made was to go with photochromics. This mostly resolves the "how do I deal with lens swapping prescription lenses without going to the poorhouse?" question. Really the only downside is that they don't work in the car (I have other, older, cheaper ones for that). As someone who frequently starts a bike ride in the sun after work and then ends up riding into deep evergreen trees and back out again, or simply rides into deepening dusk, the auto-tint feature is a Godsend.
One heads up is that the vision plan I have through my workplace, "VSP," covers some portion of any prescription eyewear (with a bunch of very complex rules, of course), but I had to fight tooth and nail to get (partial) coverage for these expensive glasses. (I think the list price all in was something like $400, and I ended up paying $250 or so out of pocket so it wasn't even that great a benefit.) Interestingly, the problem was not with the insurance company. They actually were fairly helpful and understanding. The problem was with the opticians. Basically when they agree to honor the vision plan, they sign a contract that says that they will give any customer enrolled in the plan the correct discount, just like any other medical provider. Meanwhile Oakley apparently makes all their dealers sign a different contract that says they won't discount Oakley products. In short, an optician really has no business signing both of these contracts: They can be a VSP provider or an Oakley dealer, but not both. Two different local Oakley dealers who were also VSP providers refused to honor the insurance plan and give me my discount. I complained to VSP, even going so far as to get them on conference calls to take my side with the opticians, but basically we lost the fight. I would like to think that these opticians lost their VSP contract, but I'm skeptical it went that far. Such is the power of big brand names, I guess. Ultimately they did find me a third optician who was willing to ignore their agreement with Oakley for my sake ... and they now have a regular customer.
Edit: A while back I tried some of the ones with a prescription "insert" and I thought they were worse than useless. Primarily, the things were tiny, so peripheral vision was atrocious. They also tended to snap out unpredictably. In my view (ha!) it's worth going to the trouble to find a semi-wraparound lens (see crgildart's photo of the Oakleys, above) that is a full, true prescription lens.