Can a Shimano Alfine 8 speed be reduced to 120mm hub spacing? I would like to buy a single-speed bike that happens to have 120mm hub spacing, and add the Shimano Alfine 8-speed hub. That hub, however, seems to have a 135mm spacing.

Can the 8-speed Alfine hub be modified (in less than two hours, with standard hand tools) to 120mm?
No, with either the 8 or 11 speed Alfine hub, there is no possibility of using it on a 120mm frame. The hub shell itself is about 120mm wide, without the cable carriers for shifting, or any spacers at all.

If, as it appears from your 120mm reference, you are considering a fixed gear frame with that spacing, then you should reconsider. 120mm spaced dropouts are typical on  track specific frames, or track frames from very traditional builders.

Frames like these will also have geometries which are not suited to use on the road, and I assume you don't want the bike for the velodrome, since you want gears. 

There are plenty of fixie frames with 130m or or 135mm dropouts. If it is 130mm and steel, you will have no trouble adjusting the frame to fit a 135. Otherwise, you should use a 135mm spaced frame, which likely means a hybrid or mountain bike single speed frame, or a frame with a concentric bottom bracket.