Tremolo/Vibrato Importance
Simply put... use it. It, and dynamics, are the most powerful tools in regards to conveying emotion to the listener.
In my 12-hour teaching block yesterday I found myself reminding students an awful lot to use vibrato. Long notes are a no-brainer, but also use them on shorter notes, commonly a quarter note in length (one beat), or sometimes downbeat eighth notes (the eight note on the downbeat, worth 2/3 of a beat in a shuffle or swing). Vibrato is so important that I have special notation for it to remind students commonly in the first three levels of study on the site.
P.S., using no vibrato should be thought of as a special effect... listen to the first chorus of Little Walter's "Blue Midnight" where it's almost non-existent.
Lessons on Tremolo/Vibrato can be found in the Lessons section of the site (bottom).