Mico and Barbara Beeton have already commented that using -- as appropriate -- double quotes (``/ '') or single quotes (`/') for quotes with typographic meaning will resolve your error. And Andrew Swann has suggested to use commands like \enquote from the csquotes package for marking quotes within .bib files. I'll add that for users of biblatex there's another reason to do so: Depending on your bibliography style, article titles (contrary to book titles) may be put inside (outer) quotes, which means you should use inner quotes within article titles, but outer quotes within book titles, but only for those bibliography styles. Simply using \enquote spares you the hassle of keeping track of style requirements and quote nesting levels.
\documentclass{article}
\usepackage{csquotes}
\usepackage{biblatex}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@article{A01,
author = {Author, A.},
year = {2001},
title = {An article title with a \enquote{quote}},
journaltitle = {A journal},
number = {1},
pages = {1--4},
}
@book{B02,
author = {Buthor, B.},
year = {2002},
title = {A book title with a \enquote{quote}},
location = {Somewhere},
publisher = {A publisher},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\nocite{*}
\begin{document}
\printbibliography
\end{document}

title = "``This is inside quote'' and outside quote content". Of course, if your typographic preference is to use single quotes rather than double quotes, you'd typetitle = "`This is inside quote' and outside quote content". Or, as @PLK suggests, you could elect not to use"as a field delimiter and employ{and}instead. – Mico Jul 31 '12 at 10:23"with tex will almost always result in doubled closing quotes in the output. much better to do as @Mico suggests and use intentional directional quotes, single or double as appropriate. – barbara beeton Jul 31 '12 at 12:32\qqfromtextcmdsor\enquotefrom csquotes – Andrew Swann Jul 31 '12 at 13:54