I sort of agree with all of the people saying "neither", but everyone falls somewhere on the spectrum.
I'm more of a top-down kind of guy. I pick one high level feature/point/whatever and implement it as a complete program. This lets me sketch out a basic plan and structure within the confines of the problem domain.
Then I start with another feature and refactor out everything from the original that can be used by the second into new, shared entities. Lather, rinse, repeat until application is complete.
However, I know a lot of people who are bottom up guys, who hear a problem and start thinking about all the support subsystems that they could need to build the application on top of it.
I don't believe either approach is wrong or right. They both can achieve results. I even try and find bottom up guys to work with, as we can attack the problem from two different perspectives.
