Every single argument the "moon-hoax believers" come up with is easily debunked. There is a lot of evidence to support the fact that they did go. For one thing, keeping all the hundreds of thousands of people who worked on the project in the dark (or keeping them quiet if they did know) would've been impossible. Just to touch on a few other common points:
- Hoax believers like to point out that the flag is waving. It's not in fact waving: it's swinging around because Neil was rotating the pole to drive it into the ground, and it keeps swinging for a bit because there's no air to slow it down. In fact, the way the flag behaves is completely consistent with it being in a vacuum; if this was filmed in a TV studio, it wouldn't have moved like that. It looks crumpled because they couldn't extend the arm the flag was on fully which gives the impression that it's waving (later moonlandings deliberately didn't extend it fully because they thought it looks nicer).
- Another good example is the lunar rover videos from later landings: the dust that billows up from the wheels is a perfect example of a parabolic flight path in a vacuum. In a TV studio on earth, that couldn't have happened. Nowadays we'd be able to fake that using computer animation. In 1970, they couldn't.
- The huge quantity of moonrocks brought back: the largest payload brought back with unmanned missions is a few hundreds of grams. The manned missions brought back hundreds of kilos!
- Some of the equipment they left there is still being used.
- Often pointed out is the fact that there are no stars: that's because it's filmed in daylight, and stars are very faint compared to the foreground light. A camera set with exposure to film the astronauts wouldn't be able to pick up any stars (and the astronauts themselves commented that they couldn't see them).
- Why are the shadows not completely black if there's only one light source? The moon's surface is highly reflective, it disperses the sunlight.
- Why is there not a bigger crater created by the LM's descent engine? In a vacuum there is no shockwave to propagate the effects of the engine's exhaust. Therefore the only dust that would be displaced would be directly beneath the engine.
- Why is there no rocket flame in the footage of the LM's ascent stage lifting off? The type of propellant used doesn't produce a visible flame.
- And my personal favourite: if there was even the slightest shred of evidence that it was a fake, the USSR would've jumped on it. They would've loved nothing more than to expose the US as a liar.
And why haven't we gone back (in 36 years actually, the last landing was in 1972): money. Although they did some great scientific work on the moon, what you get in return really isn't that much compared to what it costs to put a man on the moon. As early as the second landing (Apollo 12) there were debates on whether it was necessary to go back now that they'd beaten the Russians. Public interest died out (Apollo 13 wasn't even broadcast on TV until it became a disaster; nobody was interested anymore) so the US government stopped funding the missions and the planned Apollo 18 and 19 missions were cancelled.
But now, NASA is going back. By 2020, NASA plans to return to the moon, and build a settlement there for long-duration stays. The main goal: to develop the equipment and experience necessary for a manned mission to Mars.