Pumpzone has a good, short article on alignment
Check out the motor manufacturer's recommondations. Westinghouse/Teco has a good section on alignment in their manual.
The coupling manufacturer will also have limit specifications for angular and parallel alignment, and also a range for acceptable coupling-to-coupling distance.
Every so often I've run across installations where the motor and driven couplings were in good parallel and angular alignment, but nearly butted up against each other. This is a BAD idea, because, as the shafts grow due to temperature increase during operation that clearance is almost certain to be lost.
My generic rule of thumb for 50 HP and higher power is 0.001" for up to 1800 RPM, and 0.0005" for higher speeds. You can get away with more misalignment (but not much more) when rotational speeds, and power transferred is lower.
All misalignment is eventually expressed as heat, and greater stress in the mechanical system (shafts, bearings, couplings, etc.).
Time pressure to get a machine running again can't be ignored, but can't be the sole determining factor, either.
I recall an instance where a 50 HP process pump motor had at least twice in a 48 hour period snapped off several mounting bolts, and chewed through several elastomer coupling inserts. Turned out alignment was in the 0.065" range (I think the coupling was rated for 15 or 20 mil max misalignment).
In this case the entire plant went down shortly after this pump stopped operating (it's backup unit was out for repair), and we didn't have time for a spot-on alignment, but was able to get it within 10 mil using straightedge and feelers for an extra 15 minutes worth of work, and it stopped failing catastrophically.