In version 1.4.0, these are some of the things that affect respawn rates. If your version is older/newer then there are probably some differences from what is written here.
Trees and Flowers
- Trees and flowers become re-harvestable every 72 hours.
Dirt Mounds, Leaf Piles, Shells, etc.
- There's a max number that can be in the world (i.e., not in your backpack or your storage) at any given time. Shells may be the best example--if you leave a bunch of shells lying around on the beach and/or in your campsite, these will prevent new shells from spawning.
- For these purposes, the inside of your tent also counts as "in the world". I.e., make sure you don't leave shells lying around inside your tent if you want new shells to spawn.
- You'll get some new ones at the beginning of each morning, but after that the number available is governed by a refresh rate. I.e., new shells won't show up immediately after you pick up all of the existing shells.
- There are only a certain amount of each that spawn in a given day, so if you blow through them ASAP then there won't be more later in the day. (Although there isn't any reason not to blow through them ASAP, either.)
- Respawning only happens if your current play session is long enough. E.g., if you harvest everything you see in the morning then just pop your head in for 2 minutes later in the day to see if more stuff has spawned, you won't find anything. However if this second play session is longer then you'll eventually begin to find that some new things have spawned in.
- Note that things like shells will eventually get cleaned up if left lying around, even if they are shells you've picked up from the beach and put down somewhere else. So don't try to decorate with them since they will eventually disappear. (Not to mention they'll interfere with spawning as described above.)