Keep your head cool and mind relaxed. If what the other person is saying is true and you know it, then you must take it as constructive criticism instead of insult. If you know for sure that the other person is putting you down just to impose their beliefs on you or to make himself look superior, simply ignore his words.
Do not react verbally or physically. If someone is putting you down, you will not be making the situation any better for yourself by throwing a harsh word or punch in retaliation. Doing something of this sort will only make you more vulnerable, as you will be letting the other person know that he is getting to you.
Continue to be nice to them. It may be tough, but it will surely prove to be worth the effort. You do not want any awkwardness between you people, especially if you have to meet them every day, be it in class or office.
Talk to the people who put you down and ask them to quit doing that politely. If they are nice people with good intentions, they will respond positively. If their intentions are bad, then simply avoid their company as much as possible. Move away from them in class by changing your seat, or if you work in an office with them, try getting your workstation or cabin changed.
Do not let their actions get you depressed. Becoming depressed will make it even harder to deal with such people. Hold on to your confidence and keep having faith in yourself. Also note that you are so important that others are going out of their way to put you down.
Keep smiling and maintain a pleasant personality. People who put you down will surely find the excitement of putting you down disappear once they see that their actions and words are having no impact on you.