The knit CO is similar to making the knit st, but you leave the first st on the L needle and put the new stitch on there too. It can be a very stretchy CO.
The cable CO is like it, but you put the R needle between 2 sts on the L needle and wrap the yarn around it. It's got a little more structure and thickness than the knit CO, and isn't as stretchy.
The Long tail CO is fairly sturdy and can be stretchy as long as you don't pull the thumb yarn tight and leave a little space between the sts. A lot of people use it for most of their projects.
The backward loop appears to be simple, but it can be difficult to knit into and leaves loops of yarn between sts, so it's better when you just need to CO a few sts, not for the start of a large project.
sue- knitting heretic