New physics experiments appears to rule out broad classes of hidden variable theories. Here's a related article. One potentially important caveat:

Alain Aspect, a physicist who performed the first Bell-type experiment in the 1980s, thinks the team's philosophical conclusions are subjective. "There are other types of non-local models that are not addressed by either Leggett's inequalities or the experiment," he said. "But I rather share the view that such debates, and accompanying experiments such as those by [the Austrian team], allow us to look deeper into the mysteries of quantum mechanics."