In addition to Sam Dunk's (see other post) statement, there is one other part that is part of the "operating system" - for a given value of operating system: The boot loader.
When a PC (and presumably other architectures) boot up, the BIOS loads the boot sector. The BIOS is not part of the operating system. The boot sector (arguably) is. The boot sector (limited to 512 bytes!) loads the bootloader.
The bootloader may give options between different operating systems (where multiple operating systems are installed on the same computer), and/or options for loading the operating system (e.g. "Safe mode", or different run levels for Unix - q.v. etc). The bootloader then loads the (appropriate) kernel, runs it. As soon as control is passed to the kernel, the bootloader is discarded (until the next boot).
The above is somewhat simplified.
For further reading on how the parts fit together (in the case of Linux), see "Inside the Linux boot process" http://www.ibm.com/developerworks/library/l-linuxboot/ for example. The master boot record is referred to as "Stage 1 boot loader", and what I referred to as "the boot loader" they refer to as "Stage 2 boot loader".
Details will vary from O/S to O/S.