For any given Pokemon spawn point, after a Pokemon is caught there or despawned, how long does it take for another Pokemon to respawn at that point?
Pokemon spawn at my house once an hour at precisely the same minute of every hour in exactly the same location.. For example, rattatta at 1:56 pm, krabby at 2:56 pm, pidgey at 3:56 pm and so on..
Similar to what others are saying, the exact time seems to be variable. However, if you want to take a closer look at this, I recommend using Pokevision. This website can help you find Pokemon near your location and gives you the despawn time of each Pokemon.
From my experience, I notice some spots being popular for specific types of Pokemon. An example, is at the end of my street there is a house that always has water Pokemon spawning in their backyard. I've seen Krabby, Horsea, Shellder, Poliwag and even a Lapras once!
It seems like when you log in to Pokemon Go it sends a request to the server and will spawn a group of Pokemon close to you, lasting around 10 min. After that I assume they spawn at intervals but unsure how often. I would guess at a max time of 10 min, though probably more often.
They normally spawn at around 15 to 20 minutes at around where I live. They normally spawn within a 15-30km radius. That's enough to hatch 15 2.0km eggs, or 6 5.0km eggs or 3 10.0km eggs.
All pokemon seem to have different spawn rates. For example I've noticed that Mr.Mime seems to spawn near my home every 4 hours. (This I noticed first by missing it once, but capturing it the next day at the same time and also by checking pokevision and so far I've noticed it at the same spawn point at least at 5pm and 9pm every single day.) Wartortle seems to spawn once a week near my workplace. (Last weeks tuesday my workmate just missed it and this weeks tuesday we saw it in the nearby around the same time and all caught it.) Ekans I've noticed seems to spawn in a park near my home once and hour or so.
Lapras afaik seems to have more than one week spawn rate as last weeks friday I saw it near my home, but today it wasn't there at the same time. Less than a month still as I know people have caught it from the same location twice. I suspect every two weeks or so. Snorlax also has more than one week. Saw it near my home last thursday around 11am and it wasn't there yesterday. Haven't seen it in my nearby before so maybe 3weeks to a month spawn rate.