The good news is that there is no such thing as Internet death, you will probably keep on living forever even if it is only in some very dark and forgotten corner of the digital landscape. Even Lady Gagga, represented by trillions upon trillions of bits currently will reduce to a dark corner over time
Your digital accounts do have value though as they contain media that would inform later generations of your very thoughts, ideals, hopes and fears and you should be concerned that you have a plan in place to ensure the transfer of your digital assets to your family.
It is easy to ensure that your average accounts survive your death and in a few quick and easy steps you can make it easier for your family to gain control of your accounts.
The first step is to make a hand written or typed and printed list of your accounts and usernames, not your passwords.
The second step is to hand write your passwords on this list, leave enough space that you can update the password every month or two when you change your password for an account
The third step is to tell someone about the list or to keep the list with your will and you can also mention your digital assets in your will as well as deal with the disposal thereof as it is just a normal asset.
Remember that Internet domains, program code and other digital assets could be quite valuable and you do need to deal with these in your will as well.
So, the easy answer is that your google, facebook, twitter and other accounts can live forever after your death.
8 May 2012 Update:
Certain social networking sites, like Facebook, offers the option to have any account 'memorized' basically it freezes the account and no new friends can be added. Only existing friends can access the pages. As everyone knows, our friend totals decrease as we get older and this may not be an ideal solution for everyone. (Grand children and others may want to also be able to join your pages, read what you wrote, etc.)
There will still be products catering for people after their deaths, already there are quite a few start-ups dealing exactly with that topic, so watch this space.
Just a closing note on this update: You should not attach your passwords to your will. Your will becomes a public document and anyone can see it, so attach it in an envelope and add a clause in the will that the password envelope is kept sealed until given to the person you nominated to receive your accounts.
Always remember that your email account(s) and cellular phone number or other password reset communication systems can be utilized by your nominee to take control of your accounts and the working of these should be specified and the pass phrases etc. added to your password envelope.