This might sound like a trick question, but the answer is almost everybody.

Everybody that cares about image quality including but not limited to:

Graphics professionals
Web professionals
Video professionals
Other design professionals
Online shoppers
Photographers
Computer users
TV viewers
People that use their eyes

See what I mean by almost everybody?

Ok, so the professionals most of you would understand and expect it. Imagine if you told your interior designer that you wanted that one wall to be fuscia, but ended up with hot pink?

Online shoppers, ever buy a jet black purse online only to find out that it was really a dark blue?

Casual photographers want to print out those family photos from vacation in the Bahamas but their prints look like they might have picked up malaria in Africa?

Now someone out there might say: Mike, I only shoot with B/W film, and plan to digitize my photographs, why would I need color calibration?

Color calibration includes the whole entire spectrum of colors, including the different shades of gray, darkness levels and contrast.