In the early days of the Stack Overflow trilogy (including SO, Server Fault, and Super User), I noticed that many of the most active members were good contributors on all three trilogy sites. These days, with 150+ sites in the network, it's more true than ever that many people are active on several different sites.
This has led me to wonder about the possibility of cross-site badges, which would be awarded for a certain level of participation in multiple Stack Exchange sites. For example, there could be a hypothetical badge awarded for visiting each of a particular set of 3 different SE sites every day for a 15 day period. Or one for achieving 200 reputation on 5 or more sites. Or one for having an answer with +10 upvotes on each of 3 or more sites. (I'm not saying that these would be good badge criteria, just trying to provide illustrative examples.) Basically, these badges would reward people who don't limit their activity to just one site, and hopefully would encourage existing contributors who specialize in one site to branch out and look for new Stack Exchange sites to get involved in, thus strengthening the network.
Of course, the obvious problem is, which site(s) would these badges display on? Would they be associated with all the sites they were earned for, or would they display on every site at which that user has a linked account? And I have no idea what sort of problems could arise on the development side - there isn't really any other feature (that I know of) that really integrates different trilogy sites like this, so I can imagine it might be a lot of work to implement such a feature on the backend.
Is the cross-site badge idea something that people would be interested in? If the implementation details can be worked out, can we get this implemented?
Also, for the purpose of giving people on meta something to answer, what would be more good badge criteria? It's easy enough to come up with cross-site badge ideas of the form "[criteria for single-site badge] on [number] sites". What makes this feature really interesting, I think, is the possibility for badges that don't fit that pattern.