Unless otherwise stated I always use a long tail cast on. Knittinghelp.com has a good overview of different cast on methods, and here are my favourite ways to work some particular cast ons:
Provisional cast on
Any cast on done in waste yarn that can be unpicked so that the resulting live stitches can be placed on a needle and worked from or kitchener stitched. I like to work this by crocheting around the knitting needle with the waste yarn because it’s very easy to ‘unzip’ the crochet chain – this is a good video tutorial, but if you are not familiar with crocheting you may find a different method easier.
Tubular cast on
There are several ways to work a tubular cast on, which creates a very nice edge for ribbing, but this is the way I use most often. My Skelf, Gretel and Hendreary are a few patterns that feature this technique.
Judy’s magic cast on
A good alternative to the figure of eight cast on mentioned above is the magic cast on, a pictorial guide can be found on knitty.com
The invisible cast on aka casting on from the middle disappearing loop method is a neat cast on for starting in the centre of a project and working out. Techknitter has a detailed tutorial for this method which can be found here. I use it mostly for starting toys, but recently socks as well. Two patterns that use this cast on method are Trinket and Sherman.