Speaking strictly in terms of the rifle's performance and NOT the shooter's, I tailor the number of shots per group to what I am trying to to learn about a gun and how I expect to use it, then exercise a little common sense with the interpretation.
For instance, in a gun I might use for deer hunting or other large game, where I'm not likely to need more than one shot or two, I need to know where that all important first shot from a cold barrel will print. To test this, I think a three shot group is enough, assuming I make sure the barrel completely cools down between shots. In this case, a three shot group with a pet hunting load is a reliable indicator of how consistent the gun will be for that first shot in a hunting situation.
For other types of hunting, such as some types of varmint hunting or for typical range shooting, where many shots will be fired, I need to test the gun to see how the POI might change as the barrel heats up. Some guns I've shot showed little POI change as the barrel heated up, while others had a lot of POI drift. Have also had some guns that shot better with a warm barrel than a cold barrel. This is very useful information to have about a gun when it's being used this way, but I'll need to more than three shots in a group to get it. For a range gun where I will be expect to be shooting with a warm barrel (not a HOT barrel, by the way), I'll use a minimum of five shots, but even more is better.
This works for me because my shooting ability is a constant and is adequate to make a three shot group, when appropriate, a reliable test of the gun's performance. I am good enough to call my shots and therefore know the difference between a shot I pulled and a flier produced by the gun. As for gun accuracy reports I read or get from others, even reports where the gun was fired from a rest, I really don't find them very useful, simply because I have no way to compare that shooter's ability to my own. Entertaining? Yes, definitely. Useful? Not very.
Now, as a test of a shooter's skill, the more shots the better. You pretty much eliminate the luck factor with a ten shot group.
