How much value do potential employers put on voluntary/non-paid work done by an individual while they are unemployed?

Just one person's opinion - Voluntary unpaid work shows self-motivation and initiative. If you are a finance professional working on a start-up, that looks good. If you are a finance professional that is contributing your expertise to a community organization that looks great. But what does not look good is a resume where a chunk of time is missing, due to unemployment. Keep your time filled.

I agree with Regis; to take it one step further if it was volunteering for a good organization or cause (e.g. missionary work, or helped the local chapter of Red Cross) could be of value to the potential employer. It shows you care about your community and others, and you were ambitious enough to do this type of work while unemployed and looking for a new job.

I do not think the organization nor whether you were paid or not matters as much as what you did. I and other employers are looking to match skillsets to their needs. Your resume should show what you did and the successes you had just like any other job. If you are looking for a Project Manager role, talk to the massive event you PM'd for. If you are looking for an accounting role, talk to how you took on and fixed up an accounting mess.

The work done in a Professional Organization in your field helps. If you were on a standard setting committee that really counts towards your professional skill. I would always argue that you focusing on volunteering in areas that match your professional skill will build the network towards getting that next job. Those people you meet are more likely to help you get a position than anything else.

I agree as well. It shows motivation. However, need to be careful that there is real participation. Not just showing up and signing in. Potential employer may check.