"Be able to play a love song with and without vibrato." -Arnold Jacobs (via @JacobsQuotes)
Vibrato is one of the best tools we have at our disposal as musical storytellers, but it can frequently be either overused or predictable. As Mr. Jacobs stated above, it is very important to be able to play something like a love song without any vibrato at all.
A great exercise is to record a love song or melody with the vibrato, then without. If you have the ability to make the second version just as convincing as the first, you will have gone a long way towards conveying a clear story to your audience once you add it back into the equation.
Be sure to use vibrato as an enhancement, not as a music crutch.
(A fantastic performance a year ago by Harry Watters inspired me to write this blog post with lots of thoughts on vibrato.)