Is there a maximum building height in Minecraft, and why?

Yes

The Minecraft world is 256 blocks (as of Minecraft 1.2) from top to bottom. The reason for the height restriction is that the Minecraft world is made of 16x16x256 'chunks'. These are loaded into memory and rendered starting with the ones closest to the player. A 3D world of chunks (where the world is 'infinite' vertically as well as horizontally) is a whole lot more complex than a 2D world of chunks to manage, and optimizing for smooth gameplay would be a challenge. 256 is a convenient number that's a power of 2 (making it align nicely in memory).

Note that there is also a separate build height on servers. In the server.properties file, there is a property max-build-height which defaults to 256. Server admins can lower this value to prevent players placing blocks above a certain height, but it will not prevent natural terrain from spawning above this level, or players climbing natural structures above this height.

Although it is theoretically possible for a mod to increase the height limit of the map, I can't find any that work with the current version of Minecraft or are in active development.

The height in unmodded Minecraft is restricted. From the bottom of the world to the highest possible point is 256 meters, or blocks.