There are, however, many patterns that use more than one colour that are NOT stranded.
Mosaic knitting is such a technique. With this type of knitting, you never knit more than a single colour per row. Many patterns alternate two rows of one colour with two rows of a highly contrasting second colour, and use slipped stitches to create the illusion of stranded knitting. Not only is this technique easier than true fair-isle knitting, it almost eliminates the issue of tight fabric, because there are no floats. I say almost because mosaic knitting is a bit tighter than regular knitting, so the socks tend to fit small. The slipped stitches make the socks thicker and a little less elastic, and they pull in a bit. Think of those flap heels in eye-of-partridge stitch - that's what you're getting in mosaic knitting. And, as a bonus to spinners, this is a great way of combining more fragile handspun with robust millspun sock yarn!
Here are some of the mosaic socks I recently finished. I just love the eye-popping patterns you can get!
Pair number 1: this is a pattern from General Hogbuffer, one of my favorite sock designers, and it's free on Ravelry. It looks horribly complicated, but it's not all that bad. Not a beginner pattern - you do need to keep track of the rows - but well worth the effort, in my opinion. I think it looks absolutely spectacular in a bright colour combined with black.
[Pucker by General Hogbuffer, done in pink and black commercially spun sock yarn]
Pair number 2: these are my own unvention, I just used a 16-stitch mosaic pattern from Barbara Walker's stitch dictionary (I think volume 2) called "Cesar's Check". I used it in my own afterthought heel pattern, leaving a line of waste yarn where I wanted the heel, and coming back to knit it in afterwards. This is an easy way to maintain the integrity of the mosaic pattern - you don't have to think about the heel at all while you're knitting the sock. However - and this is important - if your beginning of row is at the middle of the sole of the sock, break both your main yarn colours before you knit in that waste yarn, and start with fresh ends on the row after the waste yarn. If you don't do this, you will end up with ridiculously short yarn ends to tie off and work in when you open that heel slit. I know this because I've made this mistake!! Obviously, another thing you can't do is to slip stitches over that waste yarn, so the slit has to fall between pairs of rows of the same colour. But that's not usually a big constraint.
[Cesar's Check socks with improved afterthought heel]
As I've stated, the socks will be a bit thicker and tighter than regular knitting. To take care of this, either make a size larger than you normally would (ie. instead of 64 sts, use 68 or 72), or go up a needle size.
These socks are so much fun that I've started combing through stitch dictionaries for appropriately-sized mosaic patterns.