You guys do realize that Twitter accounts can be set to "Private", right? Only the people you let in can see what you post, if you want it to be that way.
Lets say I create four private accounts; "Dad", "Mom", "Big Kid", "Little Kid". I allow all of them to see each other, but nobody else can see them. You now have an instant, anywhere-you-are, refrigerator family note system. For the record, it is also easy to send a direct message to somebody, like when Dad asks Mom to call the babysitter so they can have a romantic night out.
My friends and I (all in our mid twenties) use it for impromptu planning. Last night's BSG board game wouldn't have happened without Twitter. One quick text message, and my friend had let 12 of us know that he was getting off work earlier than expected, and were free to drop by. Five of us RSVP'd, and a fun night was had.
Lets take the idea presented by this article. I create a group of private twitter accounts: "MyHouse", "MyWasherDryer", "MySprinklerSystem", "MyModem", "MyServer", etc. My family are the only followers, and choose the things they care about to send them a SMS when an event occurs. With a proper setup back on the home side, you can direct message back to one of these accounts, and suddenly have a DIY home automation system.
I believe that the only people who haven't found a good use for Twitter yet, just aren't being creative enough with it, or flat out refuse to have anything to do with it because of the stigma that it's only used by idiots to keep up with celebrities. Give it a try, poke around for a bit, and be creative.