Even when I was young, I stood up for other kids. For myself, not so much.
Now I would absolutely stand up for myself without question. I believe I am worthy of respect and kindness, and if I'm being mistreated I would let others know.
That said, sometimes people are mean for the sake of venting their own unhappiness. If I can tell that their rudeness or cruel words is more about them then me, and they are not directly hurting me, then I do just let it go. I find adding negativity to a negative situation like that just makes me feel worse. Moving away with my head held high always makes me feel better. For instance, the other day I ran into a high school bully of mine. She wasn't rude to me, but she did make a rude comment to someone else who was walking by her. He just kind of looked at her and continued on his way, and in that case I just don't feel there is any need to say something to her. It wouldn't make a difference and it would just make you feel worse because she would come back with something rude instantly.
But, if it is directly affecting me - like with a neighbor, friend, family member, co-worker, etc., then yes - I have an easy time standing up for myself.