Why do modern windmills have 2 or 3 blades? Wouln't it be more efficient to collect most the energy within the arc as with the water pumps of old? Also, would birds avoid something more visible, as it would appear more solid?

It's all to do with the way air acts. The three winged generators have enough space between them to stop the wind from creating 'eddys' when passing through. If there were more wings, the disturbed air from one wing would cause drag on the next.

The amount of wind that they catch is a function of blade area -- not blade number. More blades would produce more turbulence. More turbulence would lead to wind forces in non productive directions and more stresses on the blades.

The reason old windmills used for pumping water or grinding grain had so many blades is because they need a lot of torque to perform their task. More blades produce more torque. Most wind turbines today produce electricity and need higher rpm than torque. It has nothing to do with turbulence.

If you haven't already noticed, more cats, windows and vehicles kill more birds than wind turbines.

All the answers given are good answers. So lets expand a little. Large turbines having up to +60ft blades have heavy loads and stress. The more blades the more stength required to support the turbine head. Thus needing stronger and larger tower bases. Blade trimming of the pitch angle allows for varies wind speeds to yield maxium effeciency without adding more mass to the structure, which is hugh already. The answer is simply bigger is costly without returns of $$$. And that is why all things that are built on a large scale. NO $$ return means no $$ invested.

Less blades, less air drag.

1 blade = cannot be, will cause wobble.
2 blades = okay. no wobble, but the covered area looks
like a slim line.
3 blades = no wobble. covered area is wider.
4 blades = about the same performance as 3 blades.

they would add more mass than the force gained

Windmills have a problem with vibration. Two blades are balanced for weight, but the reduced air flow at the bottom of the cycle causes a sideways vibration when you have an even number of blades. At least three blades is therefore best for balance.

Suprisingly, efficiency-wise, 2 blades wins over 1 blade by only 6%.
3 blades over 2 blades only gives 3% more.
It isn't cost effective to build more than three blades.

Because they do not work. If the general public found out how extremely efficient Wind Powered Generators with flat plate technology are, they would use far less fossil fuels. Hello? THINK. It is because they do NOT work that they use three aerofoil "lifting" blades.

Go read http://www.reasonablepower.com/1/know_the_facts.htm .

You are correct that it is more efficient to use the entire arch of the blade path.

If the old farmers' windmills are so illogical and their eddys are so detrimental, then they would not work and the wind turbines would work. BUT reality is the other way around. The old farmers' windmills actually TURN at low wind speed while the new wind turbines with aerofoil "lift" do NOT turn and commonly simply sit there producing NO energy at all.

And YES you NEVER heard of birds being killed or flying into an old windmill. NEVER. They still use them out west in the US and also in Australia, and they NEVER have bird kill problems.

Good question but i assume the less and lighter the blade the more faster it would spin and get more electricity than heavy and more blades putting more weight slowin down the speed of the rotation!

I would think that more blades would make it heavier and it'd take more wind to get it spinning. The amount of wind caught doesn't really matter, it's about how fast it can spin.

Perhaps it has something to do with the turbulence that the movement of each blade creates.

Another way to think about it: are the blades spinning fast enough to completely sweep through the volume of air that passes through during one rotation? If they can get some significant fraction of that volume, they are extracting about as much energy as they can (assuming the blades are well-designed)

Sandia National Laboratories screen captures:

http://www.reasonablepower.com/nice_to_know/Aerodynamic_Characteristics_from_Sandia.htm

I'm surprised that noone has mentioned Betz' Law in the previous answers. This physical law shows that the maximum energy extractable from the kinetic energy of the wind by a wind machine of any kind is 59%. If you think of extracting 100% of the energy for a moment, you will see that that means stopping the wind, which in turn means zero extraction. So we have to have some space for the wind to flow; the question is how much, and that depends on many details of blade design. The math of the situation shows that the maximum extraction occurs when the wind is slowed by the wind machine to 1/3 of its incoming velocity, which gives an energy extraction of 16/27=59%. It turns out that twisted, tapered airfoil blades can do a very good job of extracting energy (slowing the wind) by spinning at high speed (think of a fan or propeller backwards--speeding up the wind) while spanning a relatively small part of the disc. "Common sense" seems to argue otherwise, but it just ain't so. Adding more blades beyond 3 will allow greater energy extraction but by much smaller gains per blade than one might imagine. Thus, for obvious economic reasons, commercial turbines are typically made with 3 blades, remembering also that the energy stream is free of charge so slight losses of efficeincy are readily tolerable as balanced against weight, cost, and engineering issues involved with more blades.
Realize also that the situation is totally different for a commercial as opposed to a one-home domestic application. Yes, extraction of energy from low velocity wind-streams (with an "old-fashioned" farm-type windmill) may make a lot of sense for a small application. A tolerable level of economic investment can meet your one-home needs with such a system. However, the energy in the wind varies with the cube(!) of the wind speed, and a very small part of the total energy flux during the year is provided by nature in the low speed range. Therefore a large commercial installation which needs to maximize its total energy extraction and amortize rather large installation costs can easily ignore the low velocity streams if its design can accomplish efficient energy extraction by focussing on the velocity regime where the maximum energy is delivered (higher velocity). Also, higher rotational speeds are important for electricty generation. Yes, you can use gears, but every gear in a gear train represents a percentage conversion loss, so you want to get within shouting distance if possible.