We can identify absolutely convergent series with the $l^1$ space and conditionally convergent series with a subspace of $c_0 = \{\{a_n\} \in l^\infty : a_n \to 0\}$ Since $l^1$ contains all finite sequences, it is dense in $c_0$, so in this sense absolutely convergent series are dense, or "common" among all series. However, this result is not terribly illuminating, since finite sequences are also dense in $c_0$.
Are there other ways to look at the relationship between absolutely and conditionally convergent series? Maybe absolutely convergent series are meager, open or dense when we consider a more appropriate topology on the set of convergent sequences.