As was stated above, unless the engine has a starter with a slipping clutch all radials must be pulled through to ensure that there is no oil in the lower cylinders which would cause a hydraulic lock. When doing this by hand one should always go gently and stop at the first sign of resistance. On the smaller radials like the YAK's MP14, you can exert enough force to damage a hydraulically locked engine, especially if you are pulling on the end of the blade and therefore have lots of leverage.
Another occasion for pulling through an engine is if the starter is very weak. Pulling through will limber the engine making the starter's job a bit easier especially if its cold. You can also hasten the start by prestart priming. For example on a simple carburated 4 cylinder (cold), give it a 1/2 shot of prime turn the prop 1/2 a rev, and repeat 3 more times add one last 1/2 shot and hit the starter, the engine will immediately start everytime. Obviously you will have the mags off when pulling through, but you still consider the prop hot and take appropariate precautions.