Why is aniline basic and acetanilide neutral?

Basicity is due to differences in chemical structure of the 2
compounds.  Acetanilide has carbonyl (C=O) which delocalizes the free
electrons on nitrogen.  It also has phenyl ring which also "uses up"
these electons as well.  When you say that acetanilide is neutral,
that is not strictly speaking correct.  It can be protonated by a
strong enough acid, hence it can be a base.
Aniline only has phenyl ring.  It is less basic than amines without
the phenyl ring.
Amides have much lower pKa or higher pKb (measure of basicity) than amines.
Here is acetanilide structure: http://en.wikipedia.org/wiki/Acetanilide
Here is aniline structure: http://en.wikipedia.org/wiki/Aniline