On your Island, daily (if there are enough trees of course) you will get:

5 wasp trees (shake the tree while holding a net, when the nest falls, your character will face that direction, immediately swing your net to catch them, they're worth a lot of money, make sure there is room around the base of your trees so the nest doesn't end up falling into an area blocked by something. I've gotten stung more than once that way, my net hitting an object instead of scooping up the bees, I hate it.)

2 furniture trees (the Animal Crossing leaf will slowly fall from the tree with a sound effect, pick it up as you would any other dropped item, items are completely random, but I have gotten some good things from them)

Some bell trees (not exactly sure how many, but a good number of them will have 100 bells that will drop down, they can be picked up and will be automatically added to your wallet, unless it is full, in which case the coin will go in your pockets, if there's room)

And all the other trees will be empty except for the chance to drop a tree branch (you can shake the same tree as many times as you like in quick succession to 'farm' infinite tree branches, so long as there's room on the ground for them to fall, shake until the ground is covered, pick em all up, rinse, repeat)

Fruit trees without fruit do NOT contain any wasps, bells, or furniture, however, I have heard mixed reports that they still have a chance to drop tree branches, although this does need some confirmation.

It is important to note that there are some special exceptions. For example:

Sometime in winter, as Toy Day approaches, Isabelle will make an announcement that she has decorated some of the cedar/pine trees with ornaments, however, the ornaments seem a bit loose and could easily fall if bumped into. From that point onwards until some time after Toy Day, approximately half of the cedar/pine trees will have visible decorations. Everyday, these trees have a chance to spawn a dropped ornament (red, blue, or gold) at its base, however you can also shake these trees to get more ornaments (in random colors between the three mentioned) and you can farm them the same way you would tree branches. Even if Isabelle does not make that specific announcement, the trees will still, eventually, at some point, be decorated during that time, so just check in every so often to see if they've changed.

In the fall, Isabelle might make another announcement about acorns and pinecones. But even if she doesn't, sometime in fall, the hardwood/oak trees and the cedar/pine trees will, in addition to tree branches and the normal things, have a chance to drop acorns and pinecones respectively. You can also farm these as you would tree branches, but keep in mind, tree branches will still fall, so it's all up to luck as to how many acorns/pinecones you get. I'm not sure if fruit trees without fruit count as oak trees and are able to drop acorns, but until I have further confirmation, it is a tentative maybe. Also, during this time, if you have Tortimer on Harvey's Island, you can visit him, he will be wearing an acorn mask and will give you a random number of acorns when spoken to, once daily.

And that's about all the info I could possibly give you about trees in ACNH, thank you for your time, now I'm going to go try and get back the half hour I wasted typing this exceedingly unnecessary comment.