I would like to add two things to BigHoliday's rebuttal:

No Dust During Landing of the LEM
There is, of course, a lot of dust on the moon. There are also a lot of rocks. As BigHoliday noted, dust that makes it off the ground falls immediately back to it on the moon. In addition, in many places slightly below the surface is a layer of rock, which is what the LEM landed on.

Weird Shadows
Conspiracy theorists fail to take into account that the moon is an uneven surface, and as a result shadows are distorted. In one of the more common photographs "proving" this two astronauts are in the frame and one clearly has a much longer shadow than the other, and the highly uniform luminosity of the surface makes it difficult to resolve elevation detail.

The arguments for the moon landing being a hoax have been removed. I will summarize them here:

The Radiation Argument
People on Earth are protected from radiation in space by the ozone layer. So how did they survive leaving protection of said ozone layer for so long?

Extreme Heat
In direct sunlight, things get hot. Real hot. The surface of the moon will reach as much as 250 degrees fahrenheit. How did the cameras survive? How did anything survive?

No Dust Kicked Up Under The LEM
The lunar excursion module comes in for a landing and turns on that big thruster underneath to make it a little more gentle. It should have kicked up some dust - right?

No Stars In Photographs
On Earth, the atmosphere obscures stars (during the day, the sky is bright blue. unless it's cloudy). On the moon, then, even directly above the horizon is straight black with stars in.
At least, there should be stars in. Why aren't they in the photographs? Was NASA too lazy to make the fake really complete?

Shadows All Wrong
Look closely at the photographs. Shadows go all over the place! The only reason for shadows of two people in the same photograph to be so wildly divergent is if two photographs were spliced together with a light source being someplace different in both of them.

Seams in photographs
Look very, very closely at some photographs taken (particularly at the ground). If you look long enough, you'll find a seam where there's a break in the ground that clearly doesn't match up.
The rebuttal to this is that JPEG works like that sometimes, and that if you saw the original there would be no seams.