I often get this question from cognitive scientists, usually coupled with a dubious attitude. It seems worthwhile to build a collection of papers that represent success stories in the effort to use neuroscience to constrain cognitive theories. Send me your examples via email, Twitter @gregoryhickok, or as a comment to this post and I'll update this list.
How to test a cognitive theory with fMRI.
Chatham and Badre
Bridging computational approaches to speech production:...
Walker and Hickok
Greater neural pattern similarity across repetitions is associated with better memory.
Xue, et al.
What can functional imaging tell the experimental psychologist?
Amnesia and the distinction between long- and short-term memory.
Baddely & Warrington