Cannoli,
As previously posted yes use a syslog server.
You can configure this via vCenter.
You can log them to a VMFS volume, configured at ESX host level this can be very cumbersome depending on the number of hosts you have.
Look at Advanced settings/Syslog for each ESX Host you have.
However my personal favorite as it allows you to easily manage all logging for each Host is to use the vMA, this has been designed to retain the logs for a longer time and allows you to TAIL logs for troubleshooting etc.
Its a free appliance and you only require the one appliance. It not only gives you log collection but also more management functionality of your environment.
Simon Long has an excellent article, thanks Simon, on setting up the vMA as a Syslog for ESXi, This also give you the SSH access to the ESX servers and is the way I would recommend you collect and maintain your logs.
If you require a longer retention period you will need to either add extra disk storage for your logs or you could automatically copy the logs form the vMA to a corporate file share, I'm sure you can work that much out 
.
Good luck
I hope this helps.
Nathan