Yes
If you are running Lion (OS X 10.7), you can boot to the Lion Recovery partition, run Disk Utility, and erase the hard drive.
Older OS X systems - I think you could, in theory, do that in Single-user mode.
If you are erasing the hard drive, then passing on to someone else - how are they going to use the Mac if there's no operating system installed?
The good method is to connect to another Mac, using a firewire cable, then boot this Mac in Target Drive mode (restart while holding the letter T, until you see the floating firewire icon) - then your Mac should appear on the desktop of your OTHER Mac, so run Disk Utility, and erase away, if that's what you want to do.
The question remains, however. What do you do if you want to have an operating system on your old Mac? You'll need an installer for that... or, you could restore from another Mac, or restoring from another hard drive is possible, too.
Final question (really the first question) - What's your goal with erasing the hard drive? Do you just want to leave it usable, but with your own info completely gone? Or - what else?