In the medical field, the need for replication is great, given that some studies suggest that more than half of all published studies cannot be replicated. One indication of the need for replication is the existence of such articles as "Why most published findings are false." As this Science article suggests, psychological research findings are probably not as replicable as we would like to believe. This Slate article also provides a readable (and alarming) argument for the need for skeptics to do direct replications.
This cartoon makes the point that published findings may be Type 1 errors in a simple and funny way. This graphic also shows how current practices lead to publication bias. Another way to make the point is to go through 10 famous psychological findings that seem hard to replicate (from PsyBlog).
In psychology, sites that encourage replications include
APS addressed the debate about replications in a special issue that they have made available (for free) to anyone.