The lower the elevation of an object, the more disturbing atmosphere is between the observer and outer space. The ratio between this amount of atmosphere and the amount of atmosphere towards zenith is called airmass. For zenith distances of 75 degress or less and a very simple model atmosphere, the airmass is approximately given by the secant of the zenith distance. More accurate expressions can be found in the Wikipedia article about the airmass.
The seeing roughly scales with the airmass to the power of 0.6. This can only be a rule of thumb, as seeing is a very local measure and can also vary strongly across sky, depending on where the turbulent layers are. To obtain best images, one should avoid taking exposures at an airmass of 1.5 or higher (40 degrees elevation or less).
Differential atmospheric refraction
One other aspect that has to be taken into account when imaging is the prismatic effect the atmosphere has on an incoming light beam. Bluer wavelengths are refracted more strongly than redder wavelengths, which means that a white point source is spread out into a little spectrum along the elevation angle. This affects in particular exposures taken through a luminance filter, leading to elongated images.
As is shown in the Figure below, differential atmospheric refraction elongates a source by about 0.4", 1.0" and 2.0" for elevation angles of 70, 50 and 30 degrees, respectively. This is for a 400 - 700 nm bandpass luminance filter and an altitude of 2000m. For colour filters the effect is less significant, as only part of the spectrum is transmitted.
This Figure shows the differential atmospheric refraction at an altitude of 2000m above sea level. For sea level the values should be increased by about 25%. The plot is based on data presented by A. V. Fillipenko in 1982PASP, 94, 715.
Differential atmospheric refraction can be compensated by so-called atmospheric dispersion correctors (ADC). These are made of a pair of prisms (or a pair of two compound prisms) that can be rotated against each other around the optical axis.