When writing programs that do computations, my overwhelming preference is to simply write results to standard output, and to use shell redirection to capture the output in a file. In this way, I am leveraging the shell’s full functionality, in particular filename completion, in the most convenient way possible. For the file format itself, I prefer simple, column-oriented, delimiter-separated flat files. They are completely portable, and can be read and understood by most tools. (They also play well with the usual Unix toolset.)
But this simple approach breaks down, once a program has to write more than one output stream: for example in the case of a simulation run, I may want to capture periodic snapshots of the simulation itself, but also track various calculated metrics as well. These two streams will not fit comfortable into a single flat file. One option is to use a structured file format, the other option is to write to multiple files simultaneously.