Is it safe to connect and remove SATA hard drives when PC is on?

It's better not to try it if you have sensitive data on your drive. SATA data cable has 7 pins and power has 15 pins. It is all narrow down to if the drive or motherboard is capable of hot-swapping. Now, if hot-swapping is a very important feature to you, a USB or firewire cradle can be purchased for that purpose. See source for different type of SATA drive cradles. Basically, plug in the SATA drive to the cradle. The cradle itself become a hot-swappable USB hard-drive. This is known safest way to hot-swap a drive without turning off and on your computer.

Sata drives can usually be removed from you computer without any problems since they are not "hot swappable" and no problems will be caused. This however does not apply to the older IDE drives, where there is a potential risk of losing data and damaging your hardware.

A little search using a search engine will help.

NOOOOO!!!! You could risk corrupting data on the drives!! NEVER unplug or plug in a hard drive when the computer is on. ALWAYS turn the computer off, unplug it, ground it, and then install the hard drives properly.

unplugging, probably nothing will happen, BUT plugging them in....i really wouldn't recommend it, since your power supply doesn't change during system is on, it's not like your house installation, your PC power is sensitive

Don't shock your power supply

I plugged in my floopy drive while system was on, whole system stopped and floopy burned