  We generalize the ideal completions of countable discrete groups, as
introduced by Brown and Guentner, to second countable Hausdorff \'etale
groupoids. Specifically, to every pair consisting of an algebraic ideal in the
algebra of bounded Borel functions on the groupoid and a non-empty family of
quasi-invariant measures on the unit space, we construct a $C^*$-algebra in a
way which naturally encapsulates the constructions of the full and reduced
groupoid $C^*$-algebras. We investigate the connection between these
constructions and the Haagerup property, and use the construction to show the
existence of many exotic groupoid $C^*$-algebras for certain classes of
groupoids.
