What type of salt is formed when a weak acid and a weak base are mixed?

A strong acid and a strong base will ionize completely, therefore when they are mixed, they will react together to form salt and water. However, weak acids and weak bases only ionize partially. Therefore, when they are mixed, it generally results in a reversible reaction with the formation of a conjugate acid and a conjugate base as products instead of salt and water.
When a weak acid reacts with a weak base the weak acid will lose a proton and the species formed is called a conjugate base. The proton lost by the weak acid is accepted by the weak base to form a conjugate acid. So, a conjugate base is what is left after a weak acid has donated a proton in the reaction.
The reaction that occurs can be depicted as follows:          
weak acid + weak base ⇌ conjugate base + conjugate acid. A common example is the reaction between ammonia (weak base) and water (weak acid).