In Europe, is it common practice to ask an external member of your PhD committee to be a reference on a resume for job applications?
For academic jobs, I think that an external committee member is a good referee. They have read through your thesis, so they are one of the few people able to offer an opinion on the quality of your research. For non-academic jobs, I think Christiaan's answer makes sense, they aren't going to be as interested in your research but more your work-related skills.
Personally, I (UK-based) have used the external examiner of my PhD as a referee in the application for my first postdoc and in a successful fellowship application. Not being from the same institution probably looks good.
If I understand correctly, you are talking about whether to include certain references on your CV (and not about who to ask to write a reference letter for you - thanks JeffE for pointing this difference out to us).
In general, as far as I know, potential employers consult references mainly to obtain information about things not evident from your CV. That is, for example, your overall work attitude, your ambitions, whether you can work in a group, how you tackle problems, how you handle set backs, what your specific expertise is and any other personal experiences that are noteworthy to a potential new employer.
All of these things are pretty much unknown to external references. While additional references are likely welcomed, your reference list should, dependent where you are in your career, at least have one or two potential contacts that have worked personally with you.