well then we wouldn't notice anything right away other than the sun staying in one place. assuming it completely stopped spinning, the earth would still alternate dark/light sides once a year. basically, one day = one year.
then i imagine our magnetic field might do something weird, i dunno.
it would also have a HUGE effect on weather. as the spinning of the earth creates the coriolis affect which causes the spinning of hurricanes and other weather systems and currents.