What .dat files are safe to be accessed while the Bitcoin client is running? Sometimes one wants to backup some .dat files from Bitcoin, but one can't shut down the client to do so (for example, if one is running a pool). Which .dat files are safe to be copied when the client is running, and which are only updated when the client shuts down?
None of them are safe to access while bitcoind is running.  The only one that is critical to backup is wallet.dat, and the backupwallet rpc command will do that safely while bitcoind is running.