Which Tools are DIY useful?

I find that before I carry out any DIY task, I make sure I have the right tools for the job. I usually keep most of my hand tools in a tool box, hand tools are mostly screwdrivers, hammers, pliers. grips, tape measure and a torch. I also have other toolboxes with other hand tools that I do not use so much, such as files and hacksaw.
One of the most important tools that I feel that should be in a diy'ers toolkit, though not used all the time is a power drill, hopefully with a hammer action. I sometimes use battery powered tools but not that often.