Yes, but that would be a tidal effect arising from the
difference in gravitational force between the near side and far side of Earth. Since the sun normally affects earth's tides about half as strongly as the moon does, you'd still see lunar tides but with lesser extremes. Average water level would now be a little different across the globe, however, being in effect a 'sun tide' frozen in place as a permanent deformation of earth, including continental crust and ocean floor. I suppose tectonic plates would continue to drift over geologic time, so L.A. might still arrive in Seattle some day

, assuming that the ceased rotation hasn't fatally disrupted the convection of liquid magma in the mantle, on which the continental plates float about. I doubt the planet would tear itself apart -- say, a chunk of the planet breaking off and drifting sunward! After all, those same forces are already in play on the spinning earth and are not all that dramatic. The rise and fall of most tides amounts to something like one 10-millionth of the earth's radius.
The earth's orbit around the sun shouldn't change significantly with a non-spinning earth, provided that the earth's mass doesn't change, the average distance between sun and earth doesn't change, and the earth's orbital speed doesn't change. Those factors are not affected by tidal forces.
But these hypothetical scenarios are tricky.

How exactly is the earth supposed to have stopped rotating? Where'd all the angular momentum go? Was it transferred to the moon? To the earth's solar orbit? It's a conserved quantity -- it has to go somewhere, but is that even relevant to this thought experiment?
Indeed, the original question was
What would happen to life if the earth stood still? and perhaps I am hasty in taking "stand still" to mean "cease rotating". Perhaps it means completely standing still with respect to, say, the local cluster of galaxies. In this scenario, besides not rotating, the earth would no longer be orbiting the sun, either. So (depending on our motion relative to the sun) we'd either drift away forever from our life-giving sun to meet a cold, dark fate; or else we'd be drawn into the sun and quickly incinerated.

In the latter case the tidal forces might
then become great enough to tear the planet apart as it approached impact (if that's the term) with the sun, much like Comet Shumaker-Levy (sp?) was torn apart just prior to impact with Jupiter ca. 1994.