The  holonomy groupoid of  a  foliation is  another example of  a useful groupoid

it is described here:

http://www.ams.org/journals/bull/2005-42-01/S0273-0979-04-01036-5/S0273-0979-04-01036-5.pdf

For  a singular foliation see http://users.uoa.gr/~iandroul/AS-holgpd-final.pdf