There are a lot of dead Bitcoins around. This thread [1] documents about 70,000 lost Bitcoins, and you can be sure there's a lot more.
The other way to lose Bitcoins, apart from losing a wallet or forgetting its password, is to make a transaction to a bad address (as in, a valid-according-to-the-protocol address that isn't anybodies).
If I understand how it works correctly, you wouldn't fake ownership of a wallet per se; you would need to come up with private keys to match the public keys of the transactions that belong to that wallet, which I believe is equivalent to breaking SHA256. That would be unexpected. Also, there's no way to tell if a wallet is dead or just not in use (that is, all you can know is that there are transactions that have not been spent yet, and if the same address is used to receive multiple transactions you have additional information that indicates the wallet is not in use… but it can never indicate that it's dead).
If you managed to claim ownership of a dead wallet, there's nothing at all stopping you from claiming ownership of an in-use wallet too. But SHA256 is looking pretty secure right now.
As for the way Bitcoins will inevitably be lost over time, it's generally considered in the Bitcoin community [2][3] that there's nothing to worry about (it will just add a bit more deflationary pressure). I don't like this aspect of the currency — money disappearing into the void with no hope to correct for mistakes might make it perfect for computers, but it's not so good for humans.
As for tracking stolen Bitcoins, if the transaction hashes of the thefts were made public, an exchange should be able to tell if the Bitcoins that somebody is trying to turn into real money were once stolen. This is because the blockchain contains the entire history of Bitcoins — the way Bitcoins are spent is by taking the Bitcoins from a previous transaction and making a new transaction based on them; all this information is stored in the blockchain[4]. Some work has been done[5][6] at looking at what can be discovered by looking at the blockchain — it's not nearly as anonymous as many think it is.
The other way to lose Bitcoins, apart from losing a wallet or forgetting its password, is to make a transaction to a bad address (as in, a valid-according-to-the-protocol address that isn't anybodies).
If I understand how it works correctly, you wouldn't fake ownership of a wallet per se; you would need to come up with private keys to match the public keys of the transactions that belong to that wallet, which I believe is equivalent to breaking SHA256. That would be unexpected. Also, there's no way to tell if a wallet is dead or just not in use (that is, all you can know is that there are transactions that have not been spent yet, and if the same address is used to receive multiple transactions you have additional information that indicates the wallet is not in use… but it can never indicate that it's dead).
If you managed to claim ownership of a dead wallet, there's nothing at all stopping you from claiming ownership of an in-use wallet too. But SHA256 is looking pretty secure right now.
As for the way Bitcoins will inevitably be lost over time, it's generally considered in the Bitcoin community [2][3] that there's nothing to worry about (it will just add a bit more deflationary pressure). I don't like this aspect of the currency — money disappearing into the void with no hope to correct for mistakes might make it perfect for computers, but it's not so good for humans.
As for tracking stolen Bitcoins, if the transaction hashes of the thefts were made public, an exchange should be able to tell if the Bitcoins that somebody is trying to turn into real money were once stolen. This is because the blockchain contains the entire history of Bitcoins — the way Bitcoins are spent is by taking the Bitcoins from a previous transaction and making a new transaction based on them; all this information is stored in the blockchain[4]. Some work has been done[5][6] at looking at what can be discovered by looking at the blockchain — it's not nearly as anonymous as many think it is.
1. https://bitcointalk.org/index.php?topic=7253.0
2. https://en.bitcoin.it/wiki/Myths#Lost_coins_can.27t_be_repla...
3. https://bitcointalk.org/index.php?topic=109117.0
4. https://en.bitcoin.it/wiki/Transactions
5. http://arxiv.org/pdf/1107.4524.pdf
6. http://eprint.iacr.org/2012/584.pdf