How to fill holes in Hardwood Floor, Large, Medium, and Small
The only long term solution is to replace the boards. As others have mentioned, wood filler cracks out and in some cases looks like cat litter after a while. The reason is that the wood expands and contracts as the humidity changes between the seasons.

Replacing the boards is not as difficult as it seems, but the repairs will stick out unless you refinish that section of the floor. Theres a great 'this old house' video which demonstrates how to do this.

For the small gaps, the recommended solution, from a couple of floor refinishing professionals, was to leave them as character. Filling them will crack out, replacing them will be a ton of labor and may end up with the same cracks in the end - especially depending on what season you're in.