For knitting socks? Well, let's look at all the different ways.
1: One at a time on DPNs: This is all right for the person who is organized and keeps track of all changes they might have made as they knitted, and for the person who is going to turn around and make the second sock immediately after knitting the first. I'm notoriously slow about finishing anything so this method would only work if I keep track of what I'm doing.
Another way to do this is to have two sets of needles, work a bit on one sock and switch to the second-which is the way I would do this, it works better.
2: Two at a time on DPNs: Done by DKing. A perfectly valid method of knitting a pair of socks at the same time on the same needles for those who love their DPNs and can't imagine knitting socks on anything else. The only flaw with this is crossing yarns and tying your socks together. I may use this from time to time, if I had end protectors to put on my needles to keep the loops from accidentally slipping off the needles if the project is moved around. It's quite tedious to cast on and get the first couple of rounds going, but after that it goes pretty smoothly-as long as you aren't knitting and getting distracted, or you'll probably cross your yarns at some point.
The downside to this is that you can only do plain, ordinary socks using this method-no lacy patterns and no cable patterns.
3: One at a time on a circular needle: Done by the Magic Loop method. Not one of my favorite methods, but perfectly fine for Magic Loopers. Again, the knitter would have to keep track of how she did the first sock so the second sock would match.
4: Two at a time on a circular needle: Again, done by the Magic Loop method. Better for getting the socks to match. For both Magic Loop methods, it's best to have a really long needle-I would recommend a 40" one for doing a pair and no shorter than 32" for one sock at a time to keep from straining your needle ends.
5: One at a time on two circulars: Why? You'll already be using two circulars-why not do the pair on circulars, there'll be plenty of room and you'll get the socks done at the same time and they'll match. I would recommend two needles of different lengths to avoid using the wrong end when knitting the socks-a downside to this method as I've already done this at least once-but was able to fix pretty simply. The other downside would be tying the socks together by not dropping the first yarn and picking up the second-which I've also almost done at least once.
But if you'd rather still do one sock at a time, this would be the way to go, in my own personal opinion.
6: Two at a time on two circulars: I think this is my most favorite method for several reasons-some of which I outlined in the above paragraph. The most appealing reason is that I can drop the socks down to the middle of the needles when I'm not working on the them and I don't drop any stitches. The only thing I really have to watch for is tangling the yarns together, which calls for extra vigilance and not pulling too much off the ball at one time.
Yes-I've tried each of these methods at least once, which is why I can pick my favorite. I don't have anything bad to say about any of them since each knitter is different and will have their own favorite method, I'm just outlining my favorite. I don't like people who dismiss methods simply because they think it's only for showing off, and not even trying it before saying they don't like it. Some methods take more than one try to get the hang of, and I did try some of the methods more than once just so I could figure out how to use them and find out if I wanted to use them again. Since I've found my favorite I'll stick to it, just like I expect other knitters to stick by their favorite method and not tell me that my method is wrong, or too hard, or grandstanding or that I'm only doing it to show off-I don't show off, I'm merely knitting in my favorite way and if you don't like it, find something else to look at.
The only method I haven't tried is doing two-needle socks-you know, knitting them flat then sewing up the seam. I see no reason to make a pair of socks in this manner unless you absolutely cannot knit in the round using any of the methods above. I have nothing bad to say about this method, just that I don't particularly care to have to seam a pair of socks when I can knit in the round perfectly well.
You can also do the pair in this manner by knitting both socks on the same pair of needles-just don't forget to drop the first yarn and pick up the second when knitting so you don't tie your socks together.