Things have turned a little morbid here.
I imagine that if I were to cease to be alive things would mostly keep ticking over for a while. But for how long exactly?
Assuming that you've got your hosting paid for, supported, or otherwise managed that would continue to exist. But after a while domain names would start to expire, and manual intervention would be required (that is assuming that manual intervention were not required in advance.)
So when I die, I'd have to assume everything I maintained myself would disappear within two years.
Is that depressing, or realistic? I'm not sure. But definitely morbid.