I think the answers you get to this question (as it stands) will mostly reflect the types of applications designed/created by the people writing the answers. Just for example, if you're designing a program that will get data from one database (or some source anyway), massage it as needed, and then put the result into another, chances are that you're going to start by thinking about database schemas, data flow, and data encoding/formatting (probably in about that order).
On the other hand, if you were writing a typical desktop program of the type that opens a file, allows the user to edit its content, and then saves it (whether it's a photograph, word processing document, speadsheet, or whatever) chances are that database schemas won't jump to the front of your thinking. Somebody who's looked at (for example) the specs for the Microsoft Office file formats would probably have room to argue that in some cases, the design would be better if more up-front thought had been put into the format, but it usually won't be anyway.
To get a more meaningful answer, I think you need to step back a bit from simply "what is your approach to solving the problem?" to something more like: "What is the relationship between the type of problem and your approach to solving it?" Otherwise, most of what you get is usually going to be little more than an indirect statement about what kinds of problems that person has worked on.