MetaFont produces from its run three files, a metrics (TFM) file, a
generic font (GF) file, and a log file; all of these files have the
same base name as does the input (e.g., if the input file was
cmr10.mf, the outputs will be
cmr10.nnngf (the file name may be mangled if you are using an
operating system which doesn't permit long file names)
For TeX to use the font, you need a TFM file, so you need to keep that. However, you are likely to generate the same font at more than one magnification, and each time you do so you'll (incidentally) generate another TFM file; these files are all the same, so you only need to keep one of them.
To preview or to produce printed output, the DVI processor will need a
font raster file; this is what the GF file provides. However, while
there used (once upon a time) to be DVI processors that could use
GF files, modern processors use
packed raster (PK) files (incidentally, pdfTeX also uses
PK files if nothing “better” is available, but
see fuzzy fonts in PDF).
Therefore, you need to generate a PK file from the GF file; the
gftopk does this for you, and once you've done that you
may throw the GF file away.
The log file should never be needed again, unless there was some sort of problem in the MetaFont run, and need not therefore be kept.