Bohmian mechanics is a non-local hidden variable theory. It can reproduce the results of ordinary quantum mechanics. Since Bell's theorem and the subsequent experimental verdict ruled out only local hidden variable theory, Bohmian mechanics can still survive in principle.
In reality however it survives due to a different reason as pointed out by Lubos. The reason is essentially regressive. People for whom it is hard to swallow the hard reality of quantum mechanics, people who want to understand nature in terms of every day classical intuitions are the ones who often advocate Bohmian mechanics. IMHO no real physicist can support this approach. Why? The reasons are as follows.
- It violates Occam's razor by introducing extra equation in addition to the Schrödinger's equation.
- It is explicitly nonlocal and inconsistent with special relativity.
- It can not be extended to produce a quantum field theory.
- It is an unnecessary superstructure over ordinary quantum mechanics.
- The quantum mechanical spin becomes terribly messed up in this approach.
In short it is a cheap alternative to ordinary sane quantum mechanics.