What is the best method of filling the gaps in wooden floors?
If your floors are "set" meaning that the gaps are consistent through out the year I would advise the following.


the best thing you can do is add wood strips to your floor.  So you would cut out parts of the existing planks with a circular saw (set to the depth of the wood so you dont cut other things) and notch out a few planks - dremel might help here too.  Then add wood strips to fill in the blanks.  Nail them down and seal them.  You are fixing a poor install.  The wood didn't acclimate or had way too much moisture when it was shipped.  You didn't have it sitting outside right?
and if you don't want to go the permanent and correct route...  then I would personally buy some bondo wood filler, some colorant to match your existing hardwoods, and poly.  Fill your gap with the bondo to about 80-90%.  Put on a second coat (next day) with colorant that is level with floor or a little higher.  Sand it flat. Several coats of poly.  If you use cheap wood putty you will have cracking and dry ugliness.