Will Twitter ever be replaced by a decentralized messaging infrastructure that allows people to host their own data as well as send and receive messages to other people on other platforms?

"Decentralized Twitter Protocol" as the question proposes is different from SMS, Email, and Newsgroups in a very distinct and interesting way. A decentralized twitter-like protocol would require the following: UUID of a "user", a "user_user" subscription, and a "tweet" Standardization of meta-information on top of (1) including retweeting, flagging, and actions like an invitation Decentralized peer-to-peer servers where each node of data has <1% downtime. This requires data on each node be duplicated or otherwise stored somewhere else for data integrity. The structural challenge is enforcing a UUID from the creation of this system, perhaps using phone numbers as a UUID reference to build on top of. Otherwise what's to stop a one node network from creating thousands of false "users". If someone can propose a solution, it would be interesting to demo some solutions at the Data 2.0 Conference (http://data2con.com)

It seems to me that e-mail and newsgroups already provide the type of functionality you mention, but that (for better or worse) Internet users have stopped bothering with using them. What Twitter does is to provide and enforce a certain kind of structure around what can be shared -- whatever fits within 140 characters -- and in that way is perhaps more similar to SMS. In any case, I'm not certain what an alternative, open but Twitter-like messaging system would accomplish that isn't already able to be layered upon one of these existing, long-established foundations. To directly answer your question: No. Open alternatives that fit the limited criteria you specified but already exist and consumers have opted to ignore them.

From a developer standpoint, this would be awesome; however, in order to bring their business strategy to fruition, they must host user's data on their own servers, because without that precious data, there is no hope of them providing products and ad that have context to the user.  The concept you describe though is already in existence, I read an article on http://readwriteweb.com, where a developer implemented exactly what you speak of- check it out.

I believe the decentralized messaging infrastructure you refer to is better known as SMS. And no, Twitter will not be replaced by an SMS-like structure for two reasons: SMS is a lucrative market providing an incentive for many providers to enter. Tweeting is free and it is unclear how the service can earn money. Twitter's open API encourages developers to build on top of them rather than against them, coopting what could be potential enemies. Of course, a giant such as Google may always get naughty and sabotage Twitter by developing an open competitor.