Does Zombie mode in Black Ops ever end?

Solution 1:

The maps do not keep going as they are defined.

Such as the image above. However, zombies endlessly spawn which causes the game to go on until you die or quit. However, multi-player scoreboards don't seem to be able to score anything over 99.

So to answer your question, yes, zombies go on forever but the maps do not.

Solution 2:

No, it doesn't end. The difficulty keeps going up (number of zombies spawned, etc.). Presumably with some limit, though.

You're right that the maps don't keep going, although it is technically possible for maps to be generated on the fly. (Think Worms, but more complicated).