If we attach electron withdrawing groups to an amine, we can significantly reduce its basicity by removing the tendency for the electron pair of the nitrogen to attack a proton. e.g.:

The species shown above is not very basic at all due to the electron withdrawing groups.  The analogous species with three CF₃ groups is practically not basic at all.

We can also reduce the basicity by the addition of a carbonyl group (C=O), as this is also mesomerically withdrawing:

The resonance form on the right shows a positive charge on the nitrogen atom, and hence we can understand that the electron density on this atom has been reduced significantly.  Amides are very weakly basic in water because of this mechanism.  In fact, if we add another carbonyl group, we can make the amide weakly acidic.  For example: phthalimide:

It is worth noting at this point Gabriel's phthalimide synthesis:

This synthesis is a way of selectively making primary amines (other methods often result in a mixture of primary, secondary and tertiary amines which are difficult to separate).  It illustrates the acidic nature of phthalimide.