How do I seal an electrical box for a ceiling fan?

Using foam in a can, like Great Stuff http://www.homedepot.com/p/GREAT-STUFF-Big-Gap-Filler-Insulating-Foam-Sealant-16-oz-248314/100029171 can be used to fill in gaps to help prevent air leaks.

I believe that insulation falling in is less of a fire hazard than air escaping through the holes during a fire. The intent is to prevent air from flowing out into the attic space during a fire, which would create a chimney effect and continue to feed the fire oxygen.

But good news, you can achieve both with the same approach.

You want to use a fire-rated expanding foam or caulk. In the gaps within and around a ceiling box, I’d use the intumescent style of either which will expand further when exposed to heat.

Be sure to clean out any foam or caulk that works its way into the electrical box. From a code perspective, it is important to keep the volume of the box the same.

While using electrical tape to seal the holes in an electrical box is likely better than nothing, I don't suspect it will survive the heat of a fire for very long given that it is not "attached" to anything over the void of the hole. An intumescent caulk or foam will provide a much more durable blockage to prevent not only insulation from falling in, but from air escaping during a fire (which is the bigger concern IMHO).

If your boxes are metal, while the existing answers will work okay, I'd recommend first using knockout seals (sometimes called knockout covers) to fill in all the big holes, and then using caulk or foam to make it airtight. It'll be much easier than trying to fill a big hole with only spray foam.

Here's an example of a knockout seal: (Image source: Home Depot)