Every once in a while I check the motherboard manufacturer's website for bios updates. Usually the BIOS version is listed in one of the first boot screens. There are two problems with this:

First I have to reboot the machine to do this. This is not always a convenient thing to do.

Second I have to be in front of the machine. I maintain a number of servers and workstations that are spread apart geographically.

Fortunately there is a solution if the computer happens to be running Linux. From the command line I type:

sudo dmidecode -s bios-version

Here are some examples from the machines I own/maintain:
ASUS M2A-VM HDMI ACPI BIOS Revision 2101
A11

The first is a headless box that I have running in the basement. The second is from one of my client's Dell laptops.

For listing the hardware lspci, lsusb, and lshw are your friends.

On Windows some of this functionality is provided by apps like CPU-Z, though I usually just boot a Windows based machine with a Linux liveCD such as System Rescue CD, Ubuntu Live, or Knoppix.