[cheryl j (OP)]

What physics experiments could you do in space or on another planet that you couldn't do (or wouldnt want to) on Earth? And would that be a good enough reason to go there, as opposed to, say. setting up a big farm on mars.

[CliffordK]

In space it may be difficult to separate astronomy from physics. 

I do hope the future will bring large lunar based telescopes with the advantage of no atmosphere interference, and resources to build truly huge telescopes not possible in space.

Oddly, high energy particle detectors may be better on the earth than the moon, but there may be some low energy particle detectors that would benefit from a lack of atmosphere.  UV & IR Astronomy?

Another question that keeps coming up with respect to Nuclear Physics would be harvesting Helium-3 on the moon, or even from Jupiter. 

Of course for Newtonian Physics, there is always the dream of playing cosmic billiard balls, but the truth is that physics is vital in rocket propulsion and telemetry.  And, the development of newer and better types of rocket propulsion.  There is also the question of whether we could or should invest in detecting and predicting impacts between Earth and large asteroids or comets.  And, once discovered, what to do about it.

[alancalverd]

It would be fun to build a particle accelerator in space. No problems with weight, vibration, or maintaining a vacuum. Then I could offer cheap proton radiotherapy, but only to anyone fit enough to fly, so I probably wouldn't make any money. 

[PmbPhy]

What physics experiments could you do in space or on another planet that you couldn't do (or wouldnt want to) on Earth?

There is a class of experiments called microgravity experiments. In such environments you can grow special kinds of crystals and do micro-biology experiments designed for such an environment which can't be done on the ground.

See also - http://facilities.grc.nasa.gov/zerog/

[syhprum]

It is frequently proposed that large optical telescopes should be built on the moon but now that terrestrial telescopes of 30 meters or larger with adaptive optics are being built which will far out perform Hubble there seems to be little incentive.
There may be a case for radio telescopes on the far side of the moon to receive low frequencies free of interference but the cost would be very high and would yield little science.
Gravity wave receivers should work well in space if technical problems can be overcome.

[Atomic-S]

Super resolution telescopes may be possible by linking several widely spaced instruments to a common point, something not possible on Earth (yet, at least) due to atmospheric interference. This would give an effective aperture size of possibly thousands of meters. Such equipment would make the best current telescopes appear blind by comparison.