What happen if the police don't read you your Miranda rights?

Then any statements made by the defendant during custodial interrogation should be suppressed.  It does not necessarily invalidate the arrest itself. 

Many people believe that any time a person is placed under arrest they must be read the Miranda warning. This is a myth. The Miranda warning must only be given if a person is in custody and then questioned. However, once a person is in custody and questioned without being "Mirandized", then any statements so made cannot be used against them.

The 2 exceptions to this:  the statements were voluntarily and knowingly made anyway (that is the defendant waived his rights); or the questioning was incidental to the booking process (ie. name, address, etc).

Note: Any questioning before being taken into custody is legal.