Diaper bags usually have(obviously depending on a lot of factors like age, weather and breastfeeding vs. formula):
Diapers
Wipes
Change of clothes(or two) for baby
Change of shirt for mom
Snacks
Bottles
Breastfeeding cover
A few toys
Light receiving blanket
Muslin squares/burp cloth/facecloth
Sunscreen
Extra socks/mittens
Hat
Soother
Wrap or sling
But also-
Wallet
Cell phone
Keys
Anything you would normally put in your purse
I guess it really depends on you and your child as well. It is very doubtful you would have all of those things at once. Essentially for a newborn, some diapers, a travel sized package of wipes, a way to feed them and a few clean onesies or a sleeper is all you might really need for a short outing, but the other things are really handy, and once baby hits older baby/toddler aged, it gets a little more complex.
I would say just think of all the things you will be doing with your baby on a daily basis and what you absolutely need to do that.
Of course I'm not an expert, but it's what I know from being a nanny and working in the job I do all day, around babies, toddlers and their caregivers.
ETA: I found a handly list here