Don't Personalize or Internalize Disagreements
Don't take it personally. No, really -- don't take it personally. Try not to take someone's conflicting opinion as a negative assessment of you as a person or as a co-worker. It's natural for co-workers to have different feelings about projects. If someone has a different perspective, it isn't necessarily an indictment of your abilities as a human being or even as a worker.
Be open to constructive criticism, and keep in mind that turning a conflict into a learning situation may greatly benefit your career. However, if the other party is clearly making personal attacks on you, it's best to walk away from the situation.
You could, of course, respond with a personal attack of your own. Doing so is not only unprofessional but could escalate the situation to uncomfortable heights with long-term negative consequences. If the attacks on you continue, document them and consider reporting the situation to a manager or the human resources department.