This might make a fabulous setting for a science fiction novel. From Esri.com:
If earth ceased rotating about its axis but continued revolving around the sun and its axis of rotation maintained the same inclination, the length of a year would remain the same, but a day would last as long as a year. In this fictitious scenario, the sequential disappearance of centrifugal force would cause a catastrophic change in climate and disastrous geologic adjustments (expressed as devastating earthquakes) to the transforming equipotential gravitational state.
The lack of the centrifugal effect would result in the gravity of the earth being the only significant force controlling the extent of the oceans. Prominent celestial bodies such as the moon and sun would also play a role, but because of their distance from the earth, their impact on the extent of global oceans would be negligible. [...]
If the earth stood still, the oceans would gradually migrate toward the poles and cause land in the equatorial region to emerge. This would eventually result in a huge equatorial megacontinent and two large polar oceans.
(Via Boing Boing.)