Just to add to the complexity, vibrato (in frequency) also modulates
the timbre, or tone quality.  Violin bodies and human throats have
certain resonance peaks, called "formants", that are independent of the
note pitch being produced.  Certain harmonics of the note pitch will be
accentuated by being close in frequency to a formant resonance.  When a
heavy vibrato is applied to the pitch, the harmonics ride up and down
on the slopes of the formant peaks, so the relative strengths of the
various harmonics change as the note pitch slews up and down.  This
changes the perceived tone quality, and perceived amplitude (loudness).

Allegedly this is the reason why opera singers first developed such
wide vibrato (+ or minus 2/3 of a semitone is pretty wide!) -- the
variation in timbre allowed their voices to be heard over the orchestra
in a large hall.  The ear, like the eye, is more sensitive to moving
objects, and vibrato makes the tone move in quality and frequency.

Craig is mostly right -- it's hard to get vibrato without tremolo in an
acoustic instrument, and why would one want to?  The vibraphone, as the
Swedish lexicon mentions, does manage to vary volume (AM) without FM,
but it's a very recent and "technical" instrument.

Older cheap electronic organs applied pure AM tremolo, but the better
ones got FM by applying the undulating bias to the tone oscillators.
Hammond could only do AM, but they had a separate "chorus" effect,
really a form of "celeste" that made up for the lack of FM, and then
some.

--Mike Knudsen