Could life survive on a planet orbiting a neutron star? Suppose an Earth-like planet orbits a neutron star, though specifically not a pulsar. Is there any possible orbit, around any possible neutron star, in which the planet could support human life?
It is possible that there could be planets where terrestrial-type life could survive orbiting a neutron star, but they are likely extremely rare and transient.

The habitable zone where liquid water can persist around a star has a range $\approx 0.7\sqrt{L_*}$ to $1.4\sqrt{L_*}$ AU, where $L_*$ is the luminosity of the star measured in solar luminosities. The exact limits are debatable and depends somewhat on the planet's properties, but this is close enough for this answer. A typical neutron star has a low luminosity, so the habitable zone will be very close and narrow.

Neutron stars cool down very rapidly at first. A young, million-Kelvin neutron star has luminosity around 0.18 solar luminosities, but a 10 million year old neutron star is down to 0.000026, and after a billion years it will be down to a millionth of the sun. This rapid cooling means that the life zone moves inwards from around 0.3-0.6 AU for the young star to 0.003-0.007 for the 10 million year star to 0.0007-0.0014 AU for the old star. 

This means that a planet orbiting inside the zone at some time will become too cold before too long unless it is very close to the star since the zone drift slows down over time. It is hence unlikely that life would naturally be able to emerge on a planet like this, since planets that are in the habitable zone early only get a few million years before they freeze. The close planets that get a long period with decent temperature also have a period of extremely hot temperature before that, when most likely all volatiles are boiled away. 

(Given that such a system has experienced a supernova in its past, volatiles will have been reduced even further).

That said, I don't see a fundamental reason a close planet might not be terraformed with volatiles added from elsewhere. If we consider a planet orbiting a $L_*=10^{-6}L_\odot$ neutron star $10^{-3}$ AU away (that is, 149,597 km from the star) it could maintain water. It would have a period of 16 minutes. There would be some relativistic corrections to the orbit, but they are minor (we are $10^5$ Schwarzschild-radii away).  It would be tidally locked (since tidal locking happens on a timescale $\propto a^{6}$), but currently there are a fair number of atmosphere models suggesting such worlds could remain stable/ Living on the shady side would also prevent the damaging UV and X-rays, which would likely strip away the atmosphere over time. The main problem is that there would not be any geodynamic dynamo to power a protective magnetic field; this is a planet that really needs it.   

It is worth noting that there is a very different system around a neutron star that in principle (but likely not in practice) may be habitable, and that would be far away from an accretion disk. A quiescent accretion disk may have a luminosity about 1/3 of the sun, but when going active this increases by a factor of 1,000-10,000. So here one could imagine a planet orbiting at distance, getting powered by the accretion disk light. This will likely be too unstable to actually work over long periods and have the same hard radiation problem as the close one, but on paper (or in a suitable work of fiction) it is not impossible.