Note: This post has been updated with new log files for ESXi 5.1
ESXi 4 Log File Locations:
[table id=6 /]
ESXi 5 Log File Locations:
[table id=5 /]
Between version 5.0 and 5.1 the log file locations have not changed, but a couple of new logs have been added.
ESXi 5.1 New Log File Locations:
[table id=10 /]
Clearly the number of host log file has increased in newer versions, and that should make it much easier to find the log entries you are looking for. A more granular logging into different specialized log files can only be a good thing.
Logs from vCenter Server Components on ESXi 5.1:
[table id=11 /]
Just remember that ESXi only logs to memory, and that you need to set logging to a syslog server to preserve logs between reboots. If ESXi 5 is installed on local disk, the log files will be persistent through reboots, since it creates a zipped archive in /var/run/log. If ESXi is deployed via Auto Deploy, no local disk is used and the log files are not persistent, and needs to be collected by an external syslog service.