What everybody has said is spot on. The twist rate will depend on the weight of the bullet, and how long it. Bullets that aren't stabilized enough will never fly "true". It is the twisting of the bullet that gives it stabilization the same way that a gyroscope works. If the bullet is not stabilized by twist, it will tumble end over end (obviously not accurate). If they are overstabilized, the bullet may never go to "sleep" or settle into a twisting pattern around the bullets true center. Bullets that are over stabilized also don't nose over properly at the peak of the trajectory, I mentioned it in the other post about .243 twist rate. Here is a picture of what a bullet that has "keyholed" looks like.
Also something that happens when bullets are pushed very fast and they have too high of a twist rate, they sometimes just fragment and "explode" before they hit the target. You will usually see a slightly gray puff of smoke, or see fragments hit the ground and never make it to the target. This can also occur if there is a bur in the rifling of the barrel, and you are shooting thing jacketed bullets, or the jacket is badly damaged. Sometimes it just occurs from being spun too fast. Something else that is interesting is that even elevation and air density will affect the twist rate. Because of the different conditions, in less dense air, a bullet may not need quite as much twist to stabilize as it would in very dense air. There are times when shooters go to other states or locations with large differences and find out that their pet load won't shoot how it's supposed to. It's not usually a big deal, but if your bullets are right on the edge of stabilization for their weight, it does sometimes happen. It also sometimes happens that you barrel shouldn't be able to stabilize a bullet because it's too long or heavy, and the barrel might shoot that bullet better than the others. It's all quite interesting.