Can I play Call of Duty on the Xbox with someone on the PC?

No, PC and XBox cannot play CoD: Black Ops together. PC version uses dedicated servers whereas XBox version uses XBox Live.

as a rule of the thumb you cannot play FPS games cross-platform. The core of the issue the way I see it is the precision of the controls available to PC users versus aim-assist (legalized aimbot) feature on consoles. This has been a constant source for epic flame wars between PC and console players. Hard to imagine the amount of hate if they were to be allowed to play against each other.