Count number of references using biblatex

You can count references in \AtDataInput. To avoid specifying the counting/filtering criteria twice, you can create categories.

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[american]{babel}
\usepackage{csquotes}
\usepackage[backend=biber,style=authoryear]{biblatex}

\DeclareBibliographyCategory{primary}
\DeclareBibliographyCategory{secondary}
\defbibheading{primary}{\subsection*{Primary sources}}
\defbibheading{secondary}{\subsection*{Secondary sources}}

\newcounter{primary}
\newcounter{secondary}
\AtDataInput{%
  \ifboolexpr{ test {\ifkeyword{primary}} and not test {\ifentrytype{misc}} }
    {\addtocategory{primary}{\thefield{entrykey}}%
     \stepcounter{primary}}
    {}%
  \ifboolexpr{ test {\ifkeyword{secondary}} and not test {\iffieldundef{year}}
               and test {\ifnumless{\thefield{year}+0}{1980}} }
    {\addtocategory{secondary}{\thefield{entrykey}}%
     \stepcounter{secondary}}
    {}}

\addbibresource{biblatex-examples.bib}
\begin{document}
In this document, I cite \arabic{primary} primary works and \arabic{secondary}
secondary works.
\nocite{*}
% Filler text \parencite{aristotle:poetics,aristotle:rhetoric,nussbaum,hyman,pines}.
\printbibheading
\bibbycategory
% \bibbycategory is a shorthand for:
% \printbibliography[heading=primary,category=primary]
% \printbibliography[heading=secondary,category=secondary]
\end{document}

This approach also works with BibTeX as the backend. \ifboolexpr provides a flexible way to combine individual tests. Further details can be found in the biblatex manual.

A limitation is that \AtDataInput doesn't distinguish between reference sections. If your document uses these (via the refsection option or the refsection environment), you can make the counters section-specific using some commands from etoolbox.

\newcounter{primary}
\def\theprimary{\csuse{primary:\therefsection}}
\newcounter{secondary}
\def\thesecondary{\csuse{secondary:\therefsection}}

\AtBeginEnvironment{refsection}{%
  \csnumgdef{primary:\therefsection}{0}%
  \csnumgdef{secondary:\therefsection}{0}}

\AtDataInput{%
  \ifboolexpr{ test {\ifkeyword{primary}} and not test {\ifentrytype{misc}} }
    {\addtocategory{primary}{\thefield{entrykey}}%
     \csnumgdef{primary:\therefsection}{\csuse{primary:\therefsection}+1}}
    {}%
  \ifboolexpr{ test {\ifkeyword{secondary}} and not test {\iffieldundef{year}}
               and test {\ifnumless{\thefield{year}+0}{1980}} }
    {\addtocategory{secondary}{\thefield{entrykey}}%
     \csnumgdef{secondary:\therefsection}{\csuse{secondary:\therefsection}+1}}
    {}}

Here you should only access the counter values with \theprimary and \thesecondary.

Ok, so in your preamble, put

\newcounter{refs}
\makeatletter
\defbibenvironment{counter}
  {\setcounter{refs}{0}
  \renewcommand{\blx@driver}[1]{}
  }
  {We have \therefs references}
  {\stepcounter{refs}}
\makeatother

And use \printbibliography[env=counter,options for selection]

Explanation: you create a new type of bibliography, called "counter". It defined by \defbibenvironment.

1. Type of bibliography, here "counter"
2. Secund argument : what is doing at the beginning of bibliography. In your case it's: a. Reset counter b. Say to print nothing when a entry is tested.
3. What is printing at the end of bibliography.
4. What is printing / executed at each entry.

Sorry for English. If ok, say to me. I will write a french article in my weblog.

I think, you could try this :

\newcounter{reports}
\renewbibmacro*{finentry}{\sttepcounter{reports}\finentry}
\printbibliography[keyword=MyProject,type=report,title=My project reports]
\newcounter{reports2}
\renewbibmacro*{finentry}{\stepcounter{reports2}\finentry}
\printbibliography[keyword=MyProject,type=report,title=My project reports]
This year, My Project produced \thereports reports, while Another Project produced \thereports2 reports.

L.1 and L. 4 : creating counters L.2 and L. 6 : increments counters at each entry of bibliography. L. 7 : prints counter

see also http://geekographie.maieul.net/Une-bibliographie-commentee