Can I mount an harddisk without swich off the PC?

Depends on the drive type. USB, yes. Firewire, probably. Hot plugging IDE, SATA, SCSI, etc. requires specific controller, chassis, driver, and operating system support normally found in server class hardware and software.

I largely agree with Scleros, except SATA drives are designed to allow for hot-plugging. While it isn't recommended you hot-plug any drive in a PC, (server, array, etc, chassis allow for a more controlled insertion) I have done so many times for test purposes. The 5/12 v power and ground pins on SATA drives are staggered to provide a more graceful power on sequence. Still recommend powering down the system first, especially of you care about your data...