A couple on months ago I did a 1000 mile Iron Butt ride and I completed it in 18 hours.
I found if I stopped every 1 1/2 hours (for a short time) that it dramatically reduced my fatigue. So much so that at the end of the run I still had a lot of energy left.
I have taken many long trips. Gas stops are a pretty good rule of thumb. But, sometimes you need to stop more often. In '07 I rode to Costa Rica. Yes, in Central America. Last fall we rode through the Mexican Rockys and down to the end of the Baha. When the temperature is either very hot or very cold, you need to stop more often. You also need to drink plenty of fluids, preferably water. The wind will dehydrate you faster than normal when riding.
My advice is to stop whenever you want or need to. Just be sure it is a safe place to stop. Far clear of traffic. Get off and stretch. Walk around. Get a drink and maybe a snack. And be sure to take pictures so you can share your adventure with friends here on the forum. And be sure to ride safe. Don't take chances. If you are uncomfortable, STOP. If you have to hurry, you'll miss all the fun. Take your time. You may not get back down that same road again, and you don't want to miss anything. Rest as often as you need to. With me that's about every hour or 100 miles, whichever comes first. At my age you tend to look forward to the rest stops almost as much as the ride, Ha. Just kidding...
Whenever the urge hits me.
Thats one of the things i like about riding alone.
I usually stop by the side of the road in the afternoon at a rest area or whatever and light up a cigar and watch the world pass by.
My Sportster only has a 3 gallon tank. So every 120 miles. Stop - walk around a bit - get something to drink. After 10-11 hours on the road in one day, on my bike without a good long break is enough for me.
As others in this thread, I stop often when I can and enjoy places I pass through versus blasting big miles to get to a destination. I used to do the latter until the empty space between my ears recognized I was missing out on much. So I try to crank 250-350 mile days versus 500+. Will stop at road side or historical markers and such, take pics, etc.
It depends on the circumstances. I think it's safe to say you have no choice but to stop when you run out of fuel. This should be considered the longest interval for resting a bit but if time permits it appears most agree that it is wiser to stop more often.
I stop every couple of hours. Usually though it's when I need fuel. If I pass a historical marker I'll stop and read it or I stop to take a picture or two. Even standing up at an intersection for thirty seconds helps get the blood flowing again.
Stopping for gasoline is always an option as well. It depends on the temps outside too. Hydration is important. If there's something to see, I'll stop too....it all depends on how much I wanna get to where I'm going...