Cross-referencing between different files

You can use the xr package to reference to other LaTeX document.

So in chapterII.tex you say:

\usepackage{xr}
\externaldocument{chapterI}

And then can use \ref{a} like normal. You can also add a prefix:

\externaldocument[I-]{chapterI}

then you can reference it as \ref{I-a} which is useful if you have identical label names in different chapters.

Note that the normal xr doesn't add hyperlinks. It only adds the label text. The zref package can be used for this. It provides the zref-xr subpackage which gives you the same functionality and should work fine with hyperref (after all both packages are from the same author). You only need to replace \externaldocument with \zexternaldocument as well as \ref with \zref.

Note that the xr package reads the aux file, e.g. in this case, it checks chapterI.aux for references.

Beamer and xr: If you want to use the xr package to pull external references into a Beamer document, you need to be sure that the source of the references has been typeset using the hyperref package. This is because Beamer uses hyperref by default and the format of the references in the .aux file is different for hyperref. If the references are coming from another Beamer document, there is no need to do anything. If they are coming from a basic LaTeX document you may need to add \usepackage{hyperref} and typeset the source document again. As far as I can tell, there is no downside to always using hyperref.

This FAQ from the UK TUG suggests to use xr-hyper if using hyperref:

\usepackage{xr-hyper}
\usepackage{hyperref}
\externaldocument[V1-]{volume1}    % Not volume1.tex
...
... (see Volume~I, Section~\ref{V1-sIntroduction}) ...

The FAQ cites zref-xr as a superset.

Dear users of zref: please edit this answer to list some benefits of zref.