How can I include e.g., in citep

You can add prenotes and postnotes to the site with the optional arguments:

\citep{dude}
\citep[p. 42]{dude}
\citep[e.g.][]{dude}

See page 7 in natbibs manual.

When using only one optional argument (one pair of []), that becomes a postnote, when using two the first one is a prenote, the second a postnote.

In addition to the answer by Torjørn T., given that the "e.g., Author, year" format is quite common, one can conveniently define a \citeg command (to be inserted before the \begin{document}) as

\newcommand{\citeg}[1]{\citep[e.g.,][]{#1}}

which automatically produces the prenote "e.g.,".