I've been making squares lately from the Yarn Harlot's One Row Handspun Scarf.
It's a very interesting story and her pictures are wonderful.
Stephanie (the Yarn Harlot) used 5mm needles with worsted weight yarn and 26 cast-on stitches to get a 5 inch thick scarf. The pattern can be worked by adding or removing groups of 4.
I usually use aran weight yarn and 6mm needles and cast on 38 stitches.
The pattern is the same every row which is my idea of genius. It is totally reversible and absolutely beautiful. It is perfect for KAS because it knits up quickly and has a nice texture to it for those who may be a bit bored of garter stitch squares.
*K2, ktbl, P1* repeat between * * until you have 2 stitches remaining and K2
Cast on as you like (long-tail works very well for this) and knit until you have an 8" square. I use Lucy Neatby's modified conventional bind-off. It may feel odd for a minute or two but if you have a lot of binding off to do it is much faster and not as tight as a conventional bind-off. It matches the long tail cast-on very well.
ktbl = Knit through the back loop
Here's a quick video to show this for those who haven't seen this before.
See my photo page for more of this square in stripes, solids and other variegated colours. I will experiment with other weight yarns (double stranded in DK weight or Navajo ply technique with fingering weight) so feel free to PM me if you have any questions.
update: I'm working a square now in DK weight yarn. I'm doing this square double stranded and have cast on 34 stitches with 6mm needles. It is perfectly 8" square!
:)