The phrase ¡No manches! is quite common here in Mexico, and it's easy to tell from context when it ought to be used (similar to "No way!" in English), but what does it literally mean? And where is this phrase used?
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It is used to express some sort of disbelief:
No manches can be used in the following contexts:
This could be replaced with another popular phrase: ¿En serio? (Really?)
Another use would be:
The meaning of this one is like: ¡No puede ser! (This can't be happening!)
The literally meaning of "No manches" comes from the verb "manchar": (RAE)
"No manches" is interchangeable with another popular Mexican expression: "No mames". "No mames" is even more informal and "mames", from the verb mamar, is also considered a bad word.
Remember to not use these expressions in formal conversations.
From my recollection this is a polite way of saying "No me chinges" that in turn became the polite "No Manches". I grew up in Mexico City in the 60s and my family was very strict on using bad words. Its like saying fudge instead of F@#$.
The previous answers are missing an important point. It is very common in Mexico to take an expression (often a vulgar one) and replace an offending word with a similar-sounding one. This is akin to americans that shout "sugar!" when the hammer their thumbs. Thus, for instance, "caramba" is a nonsense word that replaces "carajo".
As explained by others, "no manches" can mean "no way" and "don't behave like that". Both meanings correspond also to the expression "no mames", but buy using the similar-sounding word "manches" the intention used to be to soften the expression.