It is possible to encrypt the private keys in such a way that multiple passwords are necessary to recover them. Then the encrypted password could be written down (perhaps in the will?). You could give each of several people that you trust one of the passwords. It would require collusion/cooperation among several of them to access the private key. You could choose how many passwords exist, and what percentage of them are necessary to decrypt the private key. (Example: 8 passwords, with any 4 passwords required for decryption)
Danny's on target here, I've seen a few other threads pop up on this subject.
So no, they only die with you if you want them to die with you. Just like other secrets
You can be elaborate as you like with how you create the "dead man switch" to release your bitcoin when you die.
1.
"Split" a private key or wallet password
e.g. Take a private key, write down the first 26 characters and give to your significant other, next of kin, etc.
Give the other 26 characters to your lawyer to be included in your will, with details on what exactly "it" is.
Once the will is read (after you die) the key is re-joined.
2. As DannyHamilton & isho suggested, either
multi-signature or some other encryption that involves multiple keys/passwords. There's lot of talk about multi-signature addresses on this forum, have a search!
3. Some people have talked about
time locked transactions, this is a bit complicated, personally I haven't tried doing anything like this myself. The transaction is to someone that you want to inherit some bitcoin from you, but it's crafted in such a way it can't be valid until a time in the future. When that time approaches, and you're still live 'n kicking, you move the funds to another address, and setup another time locked transaction, rinse and repeat until one day you expire, and so does the time lock...
Basically the way I see it, with time locks, it's probably a bad idea, imagine all the wasted memory on people's Bitcoin nodes if they were filled with millions of time locked inheritance transactions. Remember that these transactions won't be mined into blocks because they aren't valid "yet". You could always side-load the transaction to the recipient in a way they can store the signed transaction, and then broadcast it after your death.
But options 1 & 2, definitely sound a lot easier!