One unexpected item that became a godsend for us was an ergonomic baby carrier. We have an Ergobaby Adapt Marae, which is super comfortable and easy to use - it distributing baby's weight really well, taking the strain off your back.
We found it especially useful when our little one was a bit older and wanted to explore but needed a nap. Popping him in the carrier faced towards us, he could see the world but the gentle bouncing motion as we walked plus being so snuggly helped him drift off. It also left our hands free to push the stroller or carry other things!
Also, I know it's kinda obvious, but muslin squares - you can never have too many! Great for mopping up milk/snot/dribble or using as a little cover for privacy while feeding, and they're lightweight so they don't take up much room in the diaper bag.
We also loved our play mat. The bright colours and fun crinkly noises kept our little one entertained while we made dinner etc., and it gave him a nice safe place to roll around on when he got a bit older too.
Anything that attached to the car seat didn't really work for us - our guy wasn't too interested in toys until he could grasp things himself! But a friend swears by those toys that attach with velcro, as her little one was transfixed by them.
Hope this helps and that you get some other good recommendations - it's such a helpful thread idea!