See post #3.
What else would you spread on celery stalks?
Cream cheese.
Peanut butter butter goes well with carrots, though.
ETA: It is quite nice on celery too. I didn’t meant to imply otherwise!
peanut butter / banana sandwiches deserve a shout out. They probably came out around WWII too.
Elvis was known for pan frying them like you would a grill cheese. He may be the only one that ever did. We always had ours on either plain bread or toasted. Put a couple heaping tablespoons of peanut butter in a bowl and mash in 3/4 of a banana with a fork. spread on bread. eat the remaining piece of banana immediately. 
I had a peanut butter / banana sandwich in my lunch box throughout grade school. I still make one about once a month.
He may have been the first to popularize it, or, who knows, maybe a complete pioneer, but that’s a pretty normal way–to me, at least–to make peanut butter and banana sandwiches. In fact, the first Google entry I clicked on for “peanut butter banana sandwich” suggests exactly that method. I’m sure Elvis’s well known penchant for liking them this way led to greater awareness of this cooking method, but he’s certainly not the only one to have done them this way, not by far. (He also had bacon on his, and I’ve seen this “Elvis sandwich” on restaurant menus.)
That’s a classic kid’s snack, and I never figured out why it works so well…something about the richness of the peanut butter and the astringency of the celery. Of course, VERY few things in the world beat apple slices and peanut butter.
A few months back I was at a board gaming meetup. I had brought dinner, a PB&J and some peanut because I’m 39 and I can damned well still eat my childhood favorite if I want to. Another player noticed what I was eating and said, “Is that peanut butter and jelly?” He looked unhappy. “I’m a little…” and I was sure he was going to say “allergic.”
“…jealous.”
Cheez Whiz
Hummus, port wine cheese, cottage cheese, yogurt . . . .
Pan frying up a regular PB&J is tasty too.
A PB&J and bacon is also pretty tasty. You go the sweet and the savory.
We were eating them in elementary school before 1964.
I don’t know who invented it, but it was probably the greatest invention since sliced bread.
Yeah, I’m not one of these BACON!!! guys, but I can see that being really, really good, since I love bacon with syrup or any form of sweet on it.
Nutella.
No five year old will turn it down. A co-workers kid used to make peanut butter & Nutella sandwiches.
No one and everyone. Seriously. Very few things, especially things as obvious as food combinations, can be attributed to a lone “inventor”.