For example, let's say you want to predict movie rankings when your data is all integers in the 1 to 10 range. Classification might seem like a natural choice here, because the values are discrete, but it's actually better to use regression here because classification treats misclassifying a 5 as an 8 equal to misclassifying a 5 as a 6.
In general, use regression anytime there's a linear scale for the data. Classification is good for when there's many dimensions that don't correlate with each other well.