The 1/3 rule is what most study's say is the correct cutting procedure to use but is very seldom followed. Frequency of cut and the height of the grass would depend on what type of grass you're cutting.
Take St Augustine for example, there are nine different types of St Augustine and the cutting heights range from 2 to 4" and most are recommended to be cut at 6 day intervals, Recommended cutting height for Bermuda grass 1 to 1 1/2" at like 3 day intervals and should be done with a reel type mower. Bahia grass has a different height and the list goes on. Most all grasses have different cutting heights and intervals and if you want to throw another wrench into the works, location can play a big part.
The reason that most study's say to use the 1/3 rule is because grass clippings are 90% water and the remaining 10% is very degradable and should according to study's never bagged because grass clippings contain an estimated 4% nitrogen that can be returned to the grass plant if they are allowed to remain on the lawn. To remove more than 1/3 of the total length as someone else stated would or could supposedly shock the grass and expose the root system to sun, wind and decease and could cause permanent damage.
So what is best for your beloved lawn, I would find out what type of grass you're cutting and do a search and find out the recommended height and cutting interval.