I have a pretty horrible memory, and I'd like a simple site what I can email or SMS or enter posts about things I do, or random memories from my childhood. When I get older, I'll wish I had entered them all somewhere.
Privacy would be my main concern - I'd want to permission it only to my wife and children, and maybe a few others. I'd want my data encrypted, so admins can't even see it.
Something like this would also be great for couples - documenting relationships over time and being able to look back on them later. Emails could automatically go out on a certain date every year to remind you of something that happened on that date.
Also important would be getting my memories out. If the system ever went defunct, I'd want my data emailed to me or something.