Why does a ceiling fan usually have 3 wings?

Efficiency vs. cost, would be my guess.

Every fan, regardless of blade number needs to be balanced, so (with the exception of some exotic counterbalanced single blade fans out there), the minimum blade number has to be 2, in order to prevent the fan shaking itself from the ceiling.

There's an interesting paper here worth reading, that researches the optimum angle of attack and rotational velocity of a fan - and by extension, blade number. The results show that results show that, the maximum flow coefficient is achieved at the blade angle of attack of between 45 to 55 degrees when the number of blades was equal to 4 at most rotational velocities.

http://www.ijmse.org/Volume2/Issue5/paper5.pdf

That being said, looking at the data yields some interesting results.

What is immediately apparent in the graph above is that there is a distinct increase in the flow coefficient (a relative measure of efficiency) when the blade number goes from 2 to 3, but this levels off dramatically after that. Going from two blades to three makes sense, and also results in a better balanced fan. Four blades would be more effective, but the extra efficiency is very small, and added to that the extra manufacturing costs, extra weight, which may require a more powerful (and more expensive motor), the slight advantage becomes even less worthwhile.

In short, a three blade fan would cheaper to build, cheaper to buy, and cheaper to run than their four or five bladed counterparts, without losing much in terms of its effectiveness.

[EDIT] As an addendum to my earlier answer - if 3 blade fans are the most cost effective, then why are 4 (or more) blade ceiling fans commonly found in homes? Aesthetics and noise. The greater the number of blades (within reason), the less noise the fan will generate. 4 and 5 blade fans seem to be at that sweet spot between the amound of air being shunted around the room, and the amount of tolerable ambient noise generated.