We just returned from our first trip to the Yucatan. We neither rented
a car nor went on a tour.  We took local buses from place to place,
and used taxis in town. Taxis generally cost 30 or 40 pesos. We
started in Cancun.  We'd planned to take a bus to Playa del Carmen,
but when we got into the taxi to go to the station the driver offered
to take us to Playa for only 200 pesos.  A bargain, so we accepted. 
In Playa we rode in the car of a fellow tourist to go to the
supermarket-very handy.  We took a first class bus (ADO) to Merida
(stayed at Dolores Alba). Took another first class (ADO) bus to
Chichen Itza where we grabbed a cab to our nearby hotel.  Finally, we
took a second class bus to Cancun.  We could have just gone to
Valladolid and transferred to a first class bus, but it turned out to
be far more interesting to travel through all the small villages on
the second class bus.  At one point the driver stopped to buy some
fresh fruit for his lunch, and on the outskirts of Cancun he stopped
and hurried into a shop to buy something else.  It was really funny. 
In each case he left the engine running so the a/c kept running.  The
trip took a little longer, but it was worth the sightseeing
opportunity!
We encountered several people driving rental cars but only heard one
story.  In Playa del Carmen, on a Friday night, the driver was pulled
over for a minor infraction.  He was given the choice of showing up
for a hearing on Monday, or paying half the amount (in U.S. dollars)
on the spot, which he did. No fuss, no muss.