When you have multiple libraries you have to be very specific about when you run godep, lest you find yourself with two libraries needing different versions of a common library, for example Main imports Foo and Bar, which both import Baz. Godep provides a mechanism for handling this: each dependency is explicitly locked into a fixed revision (e.g. commit sha, in the case of git). The pain comes about when during debugging as it can be very hard to reason which version of a library you're using.
Additionally the revision aspect is also a bit of a PITA, we use a development flow which rebases our small commits into a big commit and then merges that into our master branch; if you ran godep prior to that you're now referencing a commit that no longer exists. Given the chain of references that can exist this can go a very long way down. This same pattern also forces you into needing to push your dev branches to an origin server, as godep checks out the repos during the build, which while pretty benign a concern is a PITA if you forget and your build breaks because of it.
We're strongly considering moving to "one big repo" to help combat this issue (as well as a few others) for our internal golang repositories. Referencing "published commits" in 3rd party libraries is an acceptable level of pain. We're not entirely sold on this yet... just considering it.
It seems to be a solution for some (not all) projects that are released in binary form, but that isn't relevant to most projects out there[0]. I have never felt the need for what godep provides; vendoring myself has been sufficient for the (very rare) case in which I need specific versions of dependencies other than tip/trunk.
I asked around on #go-nuts, and (though the sample size was small), the other regular contributors who idle in the channel seemed to have the same experience.
YMMV obviously.
[0] https://botbot.me/freenode/go-nuts/2014-06-19/?msg=16563763&...