I try to always weigh and consider what people tell me, especially if it has to do with possible character flaws. If several people told me that I needed to work on something within myself, I would really have to think and pray about it. God uses people in our lives to tell us things sometimes. If it's something I would be better off changing, I would definitely try.
As for non-character-related issues, sometimes yes, sometimes no. I am a people-pleaser (something I'm trying to change, HA!) so it's natural for me to adapt my clothing choices, hairstyles and other surface-level stuff (within reason) if I know it will please someone else. If someone I care about is interested in a certain TV show, game, music, etc, I will often pick up an affection for it as well in order to have more in common with the person. (This goes for relationships, family, friends, my own kids, etc.) These are easy changes that come naturally as I draw closer to other people.
Of course, some changes come happily and then there are those changes that just really aren't appealing at all. Let's face it, I'm never going to like watching sports or listening to country music.