Yeah, that's a great question.
The answer is different between Free ESXi and vSphere. For vSphere, you can set it up to notify you (thru vSphere's capabilities). Free ESXi, no such luck.
So the big thing is that even with a typical Windows or FreeBSD server, LSI's strategy for RAID card management tends to revolve around having some second system laying around that runs "MegaRAID Storage Manager" (hereinafter, "MRSM") which allows monitoring of a network of hosts with RAID cards. Normally these things also have an agent on the host that can perform some rudimentary notification operations, but this is not the case on ESXi (whether free or paid). ESXi rides the LSI short bus, which means that there's no LSI-provided mechanism to monitor the damn things, and even if you're running MRSM it may lie and report that the status is "OK" unless you actually log in with MRSM and poke around.
It's frickin' exasperating.
But ESXi does show you hardware health. And it will properly read out status assuming you've installed the LSI drivers, which I'll summarize shortly. Here's an example from a pair of boxes I installed yesterday for a client. I sent them a pair of LSI 9280's with marginal batteries, but since the write cache isn't super-important in the application, we decided to leave 'em as is.
This image shows an LSI 9280-4i4e that's almost healthy. The battery is in "partially charged" state. The volumes are in OPTIMAL state.
But this is the one I want to show you:
So here, the battery status is Unknown. I'm actually not clear on why this unit is picking it up that way whereas the other isn't. Both of the batteries are about equally dodgy.
Also, the LSI batteries are known to be rather dodgy and have a limited lifetime. If you can, avoid BBU units and instead go with the supercap based units. They're better in a number of ways.
In any case, the thing to note here is that the health status of the battery has caused the health status of "Storage" to also be listed as Unknown. If a drive had failed, this would also be showing here.
So the trick is that you have to install all the LSI stuff. It isn't super rocket science but obtaining the right stuff is a bit of an art form. You need to install on the ESXi host:
esxcli software vib install -d megaraid_sas-6.605-00.00-offline_bundle-2132901.zip
esxcli software vib install -d VMW-ESX-5.5.0-lsiprovider-500.04.V0.59-0004.offline_bundle-3663115.zip
esxcli software vib install -v vmware-esx-storcli-1.19.04.vib --no-sig-check
Plus for MRSM to work you pretty much have to disable the ESXi firewall.
esxcli network firewall set --enabled false
That last vib is actually the linchpin most people use for monitoring RAID health on Free ESXi. It has the LSI StorCLI tool as /opt/lsi/storcli/storcli which allows you to make virtually any change to the MegaRAID controller. For example,
/opt/lsi/storcli/storcli /c0 /vall show
Shows the state of the virtual drives on the first RAID controller. Smart monkeys will take this and either have a remote host monitor their ESXi once an hour by ssh'ing in and parsing the output, or will put a cron script on the ESXi host (greater difficulty level). Actually managing an array with StorCLI is a nightmare of arcane syntax invented by some masochistic hardware driver author who had no idea what "ease of use" means.
Fortunately for us, in almost all cases, replacing a failed drive is a matter of removing the failed disk and replacing it with an acceptable replacement disk. By default, an LSI controller will assume that's a disk replacement and will start a rebuild.
ESXi is not involved at all in this process. It's all the RAID controller and its onboard software. If you do need to poke at the RAID controller for some reason, then StorCLI on ESXi comes in handy for the task, or for a graphical version, MRSM from another host on the network.
I deem it a crappy overall solution, especially VMware's deficient options for alerting on Free ESXi, but one that can be made to work if you know what I've outlined here and you take the time to instrument your systems appropriately.