Every day I am at work I watch fathers pushing carts of stuff down the hall on the way to their cars. They probably came to the hospital for the birth of their child with one bag, a carseat...and maybe a pillow...and were there for four days at the most. When they leave their things have multiplied at least twofold.
So, although you might think that you are being kind and generous by bringing your friend or family member who has just given birth to a baby a gift or some flowers...remember that you are probably not the only one who had that thought AND they are the ones who have to take all of those things home. More specifically, dad is the one that has to push or carry all of those things out of the hospital because mom is not allowed to lift things that weigh more than her baby.
I do however, have a solution. When you speak to your friends or family (which I also urge you to do before showing up at the hospital...don't show up unannounced...it's possible that mom and dad have been up for days, or that mom has just had major surgery...and they have a new baby to get to know...and they might be exhausted since babies are not born with a sense of day and night), tell them that you have a gift for them but offer to drop it off at their house when they get home from the hospital. And if you do show up at the hospital and they have bunches of flowers and gifts in their room...offer to take a load home for them.
It might not seem like much, but it will save some wear and tear on a new dads back!