On pg 76 of Jech's Set Theory, he proves the existence of a nonprincipal ultrafilter on $\omega$ that is not a $p$-point.
Given a partition $\{A_n\}$ of $\omega$ into $\aleph_0$ infinite pieces, let $F$ be the following filter on $\omega$.
$X \in F$ if and only if except for finitely many $n$, $X \cap A_n$ contains all but finitely many elements of $A_n$.
If $D$ is any ultrafilter extending $F$, then $D$ is not a $p$-point.
I've been thinking why the ultrafilter $D$ isn't a $p$-point but I couldn't figure it out