How to log all Bash commands by all users on a server?

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http://askubuntu.com – Our small company runs an Ubuntu Server 11.10, to which a couple of people have SSH access. The actual terminals are sometimes used, too. How can we locally log all Bash commands run, along with user and time stamp? We can assume that no-one is nefarious and actively trying to avoid the logging, but we'd still prefer the users not to have direct write-access to their log files. Simultaneous sessions must be handled correctly. (HowTos)