It depends on the specific meaning of "rude" you're looking for:
* Impoliteness: Rudeness, discourtesy, incivility, impoliteness
* Offensive behavior: Insult, offense, affront, provocation
* Lack of manners: Bad manners, ill-breeding
* Harshness: Abruptness, brusqueness, harshness, coarseness
Example:
* "He displayed a great deal of rudeness to the waitress." (general impoliteness)
* "Her insult was completely uncalled for." (offensive behavior)
* "The children were punished for their bad manners." (lack of manners)
It's best to consider the specific situation and choose the word that best reflects the type of rudeness you're trying to describe.