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As others have mentioned, I can't think of a module that does what you describe. However, you may want to look at:
blog module (which let's each user create their own blog, and is therefore somewhat user-centric)
friend finder (haven't played with it so I'm not sure if it shows you friends based on criteria [state, category, gender, etc.] unique to each user... if it does, then it is potentially showing each user a custom query result which might serve as the basis for what you are trying to do... instead of friends that match a criteria, why not return data from the database that matches the users criteria + userID for example... I'm only guessing)
xp-weather (I think this returns your weather based on zip code, or "weather code". If that's true, perhaps you can use a similar approach to provide your desired content based on userID or other criteria)
calendar modules (I'm not sure whether any of these allow users to maintain their own unique calendars, but, if they do that might be the basis for approaches that are useful to you)
Again, I've not used these modules... so I'm only imagining what they do. But, I'm trying to narrow your search a little, which I hope is of at least a little help.
You may want to check user.php and userinfo.php (I think userinfo.php does a check to see if you are viewing your own profile... if you are, it gives you the abiltiy to update your info and access non-public account details... if you are not, it only shows info from the public profile. This might be the basis for things you are trying to do)