Usually I recommend the longtail cast on to new knitters. It's flexible, but tidy, you can start it without a slipknot, and it's versatile. I'm constantly surprised at the number of knitters who show up at classes who've never learned this method. Unfortunately, it can take a big chunk out of class time to show someone how to do it, so now when I'm teaching a class that requires it (as in a top-down sweater class), I list it as a "required" prerequisite skill.
For bridging short gaps, I like the simple backward loop cast on. It can also be used as an increase method, and for that purpose can be made to lean to the left or the right. Very useful.
Then there's the cable cast on. I use it mostly for when I want to cast on stitches at the end of a row, as in my Sandridge jacket, where it comes in handy when you are adding stitches to the front neck.
However, for my little swatch for the steeking class, I've decided to use the German twisted cast on. According to Meg Swanson, it's the preferred method when you're planning to do some corrugated ribbing. The extra twist adds depth to the base of the cast on and prevents the dreaded curling. Lucy Neatby has a great little YouTube video here detailing how to do it. Here's my little swatch in progress (and yes, I ought to have knitted the first round in order to avoid the purl blips, but it's only a swatch):
See how the edge has a little extra heft? Perfect.
