My neighbors devalued my property by putting an atv track next to it when I put it up for sale & no one wants to buy it now. Can I sue?

Sure. How much do you have? You'll need a real estate attorney. Again, How much do you have? You might just go to the county clerk & ask if he has a license for that.Then sic code enforcement on him. How much do you have? Just a general law attorney won't do.

There is nobody here that can actually give you a real answer. What you need to do is locate a local attorney that specializes in real estate and take your issue to them. Your specific location matters, along with the zoning/land use ordinances specific to that location. You maybe able to sue, you may have nothing to work with, but a local attorney would actually be able to give an answer.

Check your local laws.

Contact the zoning department. It could be in violation of the zoning.

If they are not doing anything illegal, no.

Seeing as it's not actually on your property if the track is legal than no, you have no case.

This is one of the scenarios that supports me decision to purchase property where I have no neighbors in sight. Barely within walking distance. 

And, they run the ATV's up and down the roads here, but normally it's just between farm fields. Doesn't bother me. 

Is the ATV track installed and used legally?    You didn't say.

Another moron who asks a question but leaves out the most important piece of information.

I could sue you because I think your shoes are ugly.   Would I win?   No. 

Assuming their atv track is legal, you can't sue and win.

You might be able to sue under a theory of private nuisance, but you'd have to show that noise or pollution from the ATV track is affecting your property value.