I had a case a while back where a user posted something pretty low-quality on a site I moderate. I like to give users the benefit of the doubt, so I commented on his/her post and gave some advice on how s/he could improve it. I wanted to give him a good welcome to the site.
I then found out, after some digging, that he had just finished up a month-long suspension elsewhere, and had been chat-banned in the past. He had also posted some really poor quality content on another site, where mods had not suspended him but had given him a warning.
This would have been nice to know before I interacted with the user, because I would have expected what happened next: He lashed out at me.
This is just one case where it would be great to know about suspensions or annotations to a user's profile on other sites. It would allow moderators to quickly see whether or not a user has committed infractions before and is therefore likely to do so again.
Preferably, this would show up in the Annotations section of the mod dashboard of the user's profile, where the per-site annotations would be.
Proposed changes I like:
A modification of this idea, as suggested by Undo, would be to allow moderators to choose whether or not a given annotation will enter this "global annotations" information box.
Monica's idea that seeing annotations about yourself could cause problems is a good point. One solution might be to let the folks who originally added the annotations remove them, in the case that someone is elected a moderator. Another solution is PolyGeo's idea, to have these global annotations eventually become local annotations. This also has the benefit of not shaming people for eternity. After all, people can change.