I'll discuss how property (T) gives rise to projections in maximal group, crossed product, and groupoid C*-algebras. For (non-compact) groups, these projections map to zero in the reduced completion of the group algebra. However for groupoids and group actions, this need not be the case: this is the source of the counterexamples to (strong forms of) the Baum-Connes conjecture due to Higson, Lafforgue and Skandalis. I'll discuss what happens through some simple examples, why some of these examples are worse than others, and what this has to do with exactness. The very bad examples are not known to occur for group actions, which leads to some hope that there is a way to 'fix' the Baum-Connes conjecture in this case; I'll finish by discussing joint work with Paul Baum and Erik Guentner on one approach to this. I won't assume any prior knowledge of groupoids, property (T), or the Baum-Connes conjecture.