I used to prefer thick square heels because I thought they were more stable. Then I tried a pair of plain cones. The thinner heels are a lot easier to walk in in my opinion. If you're talking about style of shoe, peep toes with sling backs.
Just give me my sneakers and call it a day. I wore heels for my brother's wedding since I was one of the bridesmaids, and swore I'd never wear them again. I like the way they look, but they aren't worth the leg and back pain.
Pumps. Pumps. More pumps. I have one or two wedge sandals every year that are just nice enough in style to look good with a dress, but I usually wear them casually. Hence the reason I have to replace them after a year. I'm not a huge fan of peep toes, but if the rest of the shoe is a solid pump, I can tolerate it. I don't like strappy sandals, mules, or slingbacks very much.
Flats. Not because I think they look best, but my knees just can't take anything other than the flattest heel. Even my riding boots, which by necessity have a very small heel, give me horrible knee pain. *sob*