Scotcher gave a fairly good explanation. I'll try to rephrase it and maybe
add to it.
When you say, "У меня есть друг", the person you are talking to learns that you DO have a friend. Therefore, you use "есть". You actually inform him or her about existеnce of a friend.

When you say "У моей сестры плохая память", the person you are talking to already knows (because it is obvious) that your sister has some kind of memory. What you are actually telling him or her is that her memory is BAD. Therefore, you don't use "есть".

"У неё новая причёска" - "She's got a new hairdo". Again, it is obvious that she always has had some kind of hair style, what you are saying is that now she's got a new one. Therefore, no "есть".