2-beat, 4-beat, 6-beat, (cha cha cha)?

keep in mind, that kicking is significantly less efficient method of propulsion than using your arms.  In a 50m sprint, then hell yeah- you're anaerobic and kick 6 beats per stroke, but for endurance swimming, where you're trying to get the most forward motion using the least amount of energy, kick only as much as is necessary to maintain body position.  For me, that happens to be an uneven, light, 4 beat kick.

i.e.- use your kick as little as possible for endurance swimming.

You get an unbalanced swim doing 4-beat kick as in 2-2 even if every other kick is just a "grace kick".

Some do a 3-1 beat kick, this is usually associated with breathing doing just one kick (but usually bigger) when breathing. 

Advanced/elite swimmers will do a 6-beat kick.

The longer the distance the less powerful the kick, as has been mentioned, it's not very efficient for propulsion so over the distance you just can't keep it up. Many advanced swimmers will do 6-beat on short distances and fall back on 2-beat on longer distances.

4 beat kick is combination or half and half of 2 beat and 6 beat in that you do one kick with one stroke, and 3 with the other arm stroke.

I did the Finding Freestyle program and gained a lot of awareness of what my legs were doing and learned to have control over it to be able to do 0-2-4-6 beat kicking.

Even though the kick gives little propulsion, isn't it vital to keeping your body in a position that maximizes the strength of your pull? If your legs are dragging, you slow down significantly, right? Isn't a kick at the very least a way to keep your legs up?

As for how many beats, if you don't care about time or form, try my method: random polyrhythms resembling bridges in Progressive rock music.