The solution for you is to use biblatex and biber's sourcemap features.
Add the following code snippet to your preamble.
\DeclareSourcemap{
\maps[datatype=bibtex]{
\map{
\step[fieldsource=url, match=\regexp{http://(dx.doi.org/|dl.acm.org/)}, final]
\step[fieldset=url, null]
\step[fieldset=urldate, null]
}
}
}
You can extend the list of URLs to be deleted by specifying the URL in match=\regexp{http://(dx.doi.org/|dl.acm.org/)}. To filter example.com, make the line match=\regexp{http://(dx.doi.org/|dl.acm.org/|example.com)}, though you should probably use match=\regexp{http://(www.)?(dx.doi.org/|dl.acm.org/|example.com)} to also catch www.example.com.
biber uses Perl's Regular Expressions, you can read more about them here.
If biber finds a match, the url and urldate are purged, otherwise nothing happens.
The MWE
\documentclass{article}
\usepackage[style=authoryear,backend=biber]{biblatex}
\DeclareSourcemap{
\maps[datatype=bibtex]{
\map{
\step[fieldsource=url, match=\regexp{http://(dx.doi.org/|dl.acm.org/)}, final]
\step[fieldset=url, null]
\step[fieldset=urldate, null]
}
}
}
\begin{filecontents}{\jobname.bib}
@article{testarto,
author = {Arnold Uthor},
title = {L'Article},
date = {2013},
journal = {Journal of Interesting Articles},
volume = {42},
url = {http://dx.doi.org/10.234/56789},
urldate = {2013-09-18},
}
@article{testartt,
author = {William Riter},
title = {Research},
date = {2012},
journal = {Journal of Interesting Articles},
volume = {12},
url = {http://dx.doi.org/10.234/56789},
urldate = {2013-09-18},
}
@article{testartf,
author = {Steve C. Ientist},
title = {Some Paper},
date = {2012},
journal = {Journal of the ACM},
volume = {12},
url = {http://dl.acm.org/citation.cfm?id=2487241&picked=prox&CFID=362895712&CFTOKEN=85933440},
urldate = {2013-09-19},
}
@online{blog,
author = {Bernie Logger},
title = {A Very Opinionated Blogpost},
date = {2013-09-12},
url = {http://www.example.com/blog/2013/09/12/opinion},
urldate = {2013-09-19},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
\nocite{*}
\printbibliography
\end{document}
yields

Edit
biber's features enable us to implement a more sophisticated handling of those URLs.
The following MWE will map DOIs, stable JSTOR identifiers and arXiv links to the appropriate doi or eprintfields. If you do not want to have those displayed, just add doi=false and eprint=false to biblatex's options.
\documentclass{article}
\usepackage{hyperref}
\usepackage[style=authoryear,backend=biber]{biblatex}
\DeclareSourcemap{
\maps[datatype=bibtex]{
\map{% JSTOR stable
\step[fieldsource=url, match=\regexp{https?://(www.)?jstor.org/stable/}, final]
\step[fieldset=eprint, origfieldval]
\step[fieldsource=eprint, match=\regexp{https?://(www.)?jstor.org/stable/}, replace={}]
\step[fieldset=eprinttype, fieldvalue={jstor}]
\step[fieldset=url, null]
\step[fieldset=urldate, null]
}
\map{% arXiv
\step[fieldsource=url, match=\regexp{https?://arxiv.org/(abs|pdf|ps|format)/}, final]
\step[fieldset=eprint, origfieldval]
\step[fieldsource=eprint, match=\regexp{https?://arxiv.org/(abs|pdf|ps|format)/}, replace={}]
\step[fieldset=eprinttype, fieldvalue={arxiv}]
\step[fieldset=url, null]
\step[fieldset=urldate, null]
}
\map{% DOIs
\step[fieldsource=url, match=\regexp{https?://dx.doi.org/}, final]
\step[fieldset=doi, origfieldval]
\step[fieldsource=doi, match=\regexp{https?://dx.doi.org/}, replace={}]
\step[fieldset=url, null]
\step[fieldset=urldate, null]
}
\map{% get rid of
\step[fieldsource=url, match=\regexp{https?://(dl.acm.org/)}, final]
\step[fieldset=url, null]
\step[fieldset=urldate, null]
}
}
}
\begin{filecontents}{\jobname.bib}
@article{testarto,
author = {Arnold Uthor},
title = {L'Article},
date = {2013},
journal = {Journal of Interesting Articles},
volume = {42},
url = {http://dx.doi.org/10.234/56789},
urldate = {2013-09-18},
}
@article{testartt,
author = {William Riter},
title = {Research},
date = {2012},
journal = {Journal of Interesting Articles},
volume = {12},
url = {http://dx.doi.org/10.234/56789},
urldate = {2013-09-18},
}
@article{testartf,
author = {Steve C. Ientist},
title = {Some Paper},
date = {2012},
journal = {Journal of the ACM},
volume = {12},
url = {http://dl.acm.org/citation.cfm?id=2487241&picked=prox&CFID=362895712&CFTOKEN=85933440},
urldate = {2013-09-19},
}
@online{blog,
author = {Bernie Logger},
title = {A Very Opinionated Blogpost},
date = {2013-09-12},
url = {http://www.example.com/blog/2013/09/12/opinion/},
urldate = {2013-09-19},
}
@online{HawSpT,
author = {S. W. Hawking},
title = {The Nature of Space and Time},
date = {1994-09-30},
url = {http://arxiv.org/abs/hep-th/9409195},
urldate = {2013-09-19},
}
@online{HelfGold,
author = {H. A. Helfgott},
title = {Major arcs for Goldbach's theorem},
date = {2013-06-14},
url = {http://arxiv.org/abs/1305.2897v2},
urldate = {2013-09-19},
}
@article{FregeNumber,
author = {G. Frege},
title = {The Whole Number},
journal = {Mind},
series = {newseries},
volume = {79},
number = {316},
pages = {481-486},
date = {1970-10},
url = {http://www.jstor.org/stable/2252434},
urldate = {2013-09-19},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
\nocite{*}
\printbibliography
\end{document}

doi. You can map specific URLs to thedoifield as explained in Biblatex: Convert doi-url into doi field, that particular solution maps certain URLs to thedoifield, it can easily be modified to dispose of those URLs though. – moewe Sep 18 '13 at 06:37