Could be several things.  Could be a wheel bearing, could be a wheel out of
balance, could even be a warped brake rotor, could be a worn tie rod end.
Likely, the reason it stops is because by tapping the brake or by letting
off the gas, you decelerate slightly below the speed at which all the black
magic forces of imbalance come together.  Speeding up could even change the
symptoms.

Should be a cheap enough thing to take to a garage and have diagnosed if
you're not incline to do such things yourself.  None of the things I
mentioned above are terribly expensive or difficult to do yourself if you
possess a little mechanical ability, except balancing a wheel.  That has to
be done on a machine - any tire shop can check and balance a wheel.  Usually
about $10 per wheel.  If it were a wheel bearing (lower on my "most likely
list"), the parts are around $100 and it can be replaced in your driveway,
albeit with a good deal of grunting.

Hope this helps... of course it doesn't.  It just made your list of things
to look at bigger...