Is it legal to build a fence across an alley?

No. An alley is not private property and is there for access by all. If you built a fence across the alley others would not be able to use it. In many cities the garbage collection is done using alleys.

Another View: The above answer would apply if the alley was a "public way."

While there ARE such things as 'private' alleyways, caution must be used if you own it and decide to close it off. If it has been used for a certain period of time (set forth in your states laws) as a thoroughfare by the public (even though it IS private property) you may not legally be able to close access to it without notice.