A conjugate base is formed when an acid loses a proton (H$^+$). The ammonium ion (NH$_4^+$) is a weak acid that donates a proton to form NH$_3$:
\[
\text{NH}_4^+ \rightarrow \text{NH}_3 + \text{H}^+
\]
Hence, NH$_3$ is the conjugate base of NH$_4^+$.