Toe-Up Socks
I have expressed before that I kind of hate the way that toe-up sock toes look, because no matter what method you choose, the toes end up square and pointy and really duck-bill-looking, which is not the way my feet or any of my other socks are shaped. What I didn't mention here, is that a few months ago I came upon a pretty workable rounded toe.
I keep misplacing the scrap of paper I wrote it on, but basically you start it like any other toe-up sock but with a few more stitches - traditional cast-on methods call for a total of 16 stitches cast-on, and I start this one with 20. It doesn't matter how you cast them on, just make sure there are 20 stitches.
So, your typical toe says to knit the first round plain, then knit the second round as K1, M1, knit to last stitch on first needle, M1, K1, K1, M1, knit to last stitch, M1, K1. You alternate between these two rounds until you have your prescribed number of stitches, and your toe is angular and probably too narrow for anyone with feet bigger than a women's size 6.
For my rounded version, you still knit the first round plain, then knit the second round as K1, M1, K1, M1, knit to last two stitches on first needle, M1, K1, M1, K1, K1, M1, K1, M1, knit to last two stitches, M1, K1, M1, K1. Depending on the size of sock you are making, you alternate between these two rounds a total of two-four times until you have about two-thirds of the total number of stitches needed for the foot. (I usually use two for my size 8.5 Women's feet and four for my husband's size 13 Men's feet, your mileage may vary.) At this point, switch to the regular increase round described in the previous paragraph and alternate between a plain knit round and that until you have the prescribed number of stitches.
Increasing twice at each end of the needle is kind of a pain in the butt, but the toe looks so much nicer and feels way more comfortable on my feet.