In this video of "Breaking Bad", beginning at 0:21, Mike uses what looks like a Phillips screwdriver, but presses the tool to turn the screw. I always wanted one of these; what's the name of this type of tool?
That is a push pull ratchet screwdriver. It has a spiral shaft mechanism that turns the push/pull into rotary motion.
This would be a relatively bad choice for any new holes (e.g., screw into wood where there is no existing hole), because it could easily slip. But I see two good uses for it (besides the "really cool movie use", of course):
Arthritis or similar problems - Turning a screwdriver can be hard on the fingers and the wrist. Pushing is much easier. For some people, this could make the difference between doing the job themselves pain-free or doing in a very painful way or having to get help from someone else. Power tools are a common way around this type of problem, but they have additional costs and those tools are often much heavier, which can exacerbate the same type of physical problems.
Tight spaces - There are places (the movie clip is not one of those) where you have limited room to work and a screwdriver like this will help get the job done without repeatedly scraping your knuckles/pinching your fingers/etc.