Based on our current understanding of physics, latency would make two-way communication impractical. Even if you were willing to wait around a few thousand generations for the metaphorical ACK, you're not likely still interested in the response to your request. As far as I can tell, the only form of communication that would be relevant would be one-way broadcasts. Because of this, I would envision some kind of intergalactic CDN, continually updating caches in distant galaxies with the historical events of their senders. This information could then be queried by hosts within the neighborhood of these caches.

That said, I wouldn't want to be the one to aim that link... or stand anywhere near a transmitter powerful enough to be detected at intergalactic ranges. You'd probably need some kind of system that obscured the light of a very bright star in order for that to work.