In psychology voting on which studies should be replicated is established on a website. The ReplicationWiki (that I founded) offers a voting option for studies in economics and related fields, but it is not yet used much. I already saw a couple of questions on specific papers here in the academia stack, in the cross validated stack (c1, c2, c3), and in the quantitative finance stack, and added the studies to the wiki and a link to questions here (1, 2, 3, c1, c2, c3, quant).
There are many other places where such questions on replication of specific studies can be found, e.g., in the forums for specialized software (d). To get further suggestions I would like to know if you have already replicated studies yourself or with your students. What would you think would be a mechanism that motivates to share such experience and help to identify the studies that should be replicated? And the replications that are already available somewhere but not yet listed in the wiki? Where would be the right place to ask?