One way to find out is to examine the belt. If a V-belt is full of tiny cracks, frayed, has pieces of rubber missing, is peeling or otherwise damaged, it needs to be replaced -- NOW. Also, if a belt is oil soaked or "glazed" (hard shiny appearance on the sides of the belt) it also needs to be replaced. Either of these two conditions can cause the belt to run hot, which can weaken it and increase the danger of it breaking.
Unfortunately, a visual inspection alone isn't a sure-fire method of determining the true condition of a belt because internal wear that you can't see is just as important as external wear that you can see. All belts are reinforced with cords. The cords are what give the belt its strength and keep it from stretching or breaking. But as a belt ages, the constant flexing, heat and strain weakens the cords. Eventually the cords reach a point where failure can happen suddenly and unexpectedly. The belt may still look good as new on the outside, but be on the verge of snapping internally because the cords have lost their strength.
So the other factors that need to be considered when judging the condition of a V-belt include the belt's mileage and age. A V-belt that's more than three or four years old and has more than 40,000 or 50,000 miles on it may be a belt that is nearing the end of its useful service life. For this reason, you might be well advised to replace a high mileage belt even if it still looks okay.