One counter-argument I've heard is the idea of "scaffolding": The system may have had other supporting parts in earlier stages of evolution; those parts have since disappeared. What's left behind is "irreducible" since you can't take anything away and still have a working system. But that doesn't refute evolutionary theories, because evolution itself is not purely additive. You might need to add parts (not just "reduce" them) to get from the current state to an earlier state.

This website addresses the scaffolding idea, but it isn't very well written. Do you know of any better resources? http://www.ccrnp.ncifcrf.gov/~toms/paper/ev/behe/

Do you know of any specific examples?

This page claims to give some examples: http://www.don-lindsay-archive.org/creation/evolve_irreducib...

However, since this forum is populated mostly by computer programmers and entrepreneurs (including myself) rather than biologists, I find it's not a particularly advantageous place for discussing such topics. I probably shouldn't have waded into this thread to begin with. Please forgive me if I flag and move on.