Depends on a few factors but generally 5 - 10mph will do it, you'll probably see porosity in the finished weld!

I especially agree with Jon about the wind speed, and that other factors are involved. For example, if your shielding gas flow is too little, it will take less wind speed to blow the shielding away. If your gas flow is too great, you can actually form a vortex that will promote oxygen and nitrogen into the weld pool regardless of the wind speed. Being concerned about the wind speed is certainly important, but just in my personal opinion, your main concern should be proper shielding gas flow.

5mph or 8 kmh as stated in AWS D1.1 structural code. You can erect a small "hooch" or shelter around the area directly adjacent to the weld and you would be okay as long as you have adequate ventilation.

As has been stated, 5 mph is the max allowed by AWS D1.1. Also stated by others, it might not take 5mph to cause problems if the gas flow rate is on the low side.
As far as blocking the wind, many ideas will work. Blocking the wind with your body might be enough sometimes, or you can rig up tarps, move the welding indoors or behind a building, etc.

To see an extreme case of what happens when shielding gas is blown away, try running some beads on scrap metal with your gas shut off. The resulting "metal foam" is one result.

Anytime you are getting porosity, you should check for exposure to wind or draft and check your gas flow. (Other things can cause porosity, like welding over oil or dirt, incorrect welding parameters, etc., but you asked about shielding gas.)

Something that is often overlooked is too much angle on the welding gun. If tipped too far, you will get a venturi effect where the gas flows past your weld zone and pulls air in with it. The gun should be within 15 degrees (drag or push) of a right angle to longitudinal weld axis. You can get away with more angle, just remember that the chances of losing gas coverage becomes greater. No big deal; that's what grinders are for, right?

Chet