"No touch" is not really grammatically correct, but sometimes English-speaking parents say this to children to instruct them not to touch something.
"Don't touch" is the correct way of asking someone not to touch something.
However, sometimes you might see a sign (at an art gallery or a zoo, for example) that says "No Touching." This is also grammatically correct, but in speech it generally means "Don't touch anything," rather than "Don't touch this thing."