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