Simon Long has published a great blog on log files in ESXi 4.0. It goes over the primary log files in ESXi 4.0, and the various ways to obtain and view them. If you're used to logging into the COS on classic ESX to view these files, then please do read this entry to see various alternatives for doing this in ESXi. One of my favorites is with a web browser, because you can scroll through an entire log file pretty easily, and use the web browser's built-in search capability to look for a particular string.
One question raised by Simon is, how do you obtain the HA logs (aka AAM logs) on ESXi, since they are not exposed through the various means described. The answer for this is to use the "Export System Logs…" option in the vSphere Client. This will download the usual "diagnostics bundle" which contains all available log files, including AAM, and you can then view the contents locally by opening the archive file.
Thanks to Simon for putting this together.