I would probably take it to management.

I live in an old old house (100 years) that is split up into five apartments.  One neighbor has a newborn and a school aged kid.  I NEVER hear that baby unless I am outside and they have the windows open and then it often sounds like a crying cat. ;)

I DO, however, hear the couple that plays ball with their dog at 3 am (seriously! wtf) ... you know  that very distinct sound a bouncing rubber ball or tennis ball makes as it first hits, then again, then "dribbles" down slowly to a stop.  Yeah, all the damned time I hear THAT.  And the woman's high heels clomp clomp clomping like a horse up there.  Or their crappy dance / club music bassline.  I hear all of that from the childless couple, and nothing from the ones with a kid and a newborn.

So, I think that a certain amount of tolerance is necessary when you live in an apartment but it depends on how excessive the noise is and if it is happening late at night or not.   I grew up living in a lot of apartments, up and down, and my mother didn't make me be *silent* but she did always caution me to remember that other people lived there too and it sounds like if your neighbors were at least considerate then it wouldn't be so loud.  You just can't carry on as if you lived in a house all on your own, kids or not, when you live in an apartment.  No one expects little kids to be silent but I think that a parent should try and get them to at least be moderate in their running/stomping/screaming or try and take them outside more often. .   Just my 2 cents anyway, I think people are obligated to at least try and "keep it down".  Especially when they're in an upstairs unit!

I agree with the open mindedness and I have been trying that for most of this time. I just get nervous as to what might happen when I am sleep deprived and a new parent that just got their baby to sleep. @Charlotte_Sometimes I agree with you about explaining to kids that they need to be a little considerate. I understand we live in an apartment and that noise from other people is to be expected. I even understand that kids make noise.. But this is over the top sometimes..We have a shelf hanging on our wall with glass ware hanging from it that shakes every time one of them runs. (these kids are around the ages of 5 and 2 btw, so I think explaining to them that they live with other people in the house is not completely out of the ordinary)

And FTR - It all usually stops at about 930-10ish at night (I think I am just as happy as their mother when they go to bed) BUT it does happy sometimes early in the morning and when it is happening after 7 is does not stop until they are in bed. 

I would recommend just starting early with explaining to them that other people live there too.

I just remind the kids that other people live here too, and would they want to be working up early by someone running down the stairs yelling?  For some reason they all race to the car and yell "I win" at 8:00 in the morning when I take them to school. I'm constantly reminding them to keep it down, and I think that generally they are quiet, but they do act up once in a while..they are boys ages 13, 10, and 10 lol. They get some serious pillow fights going on and I fear for my stuff!

@calliopemarie the crazy thing is..these ARE the first floor neighbors! At first (which is why we said something nicely) we figured they just didn't realize the noise travels that much. But after telling them about it, it gets to the point that you just figure they don't care. @curious - that's a good point, I always forget the baby can pretty much hear everything I am hearing. I actually don't think it's going to register that there is an actual baby in me until he pops out! Weird, I know.