I would like to erase everything on my Mac's hard drive as I'm going to recycle or sell it. Is there a way to do it without OSX disc?
Target Disk Mode
If the Mac you want to erase supports Target Disk Mode, and you have a second compatible Mac (you need to use either Firewire or Thunderbolt on both), you can use the second Mac to erase the target one. Boot up into Target Disk Mode (hold down T), and the target Mac will appear as an external drive on the second Mac. Then you can run Disk Utility to wipe the drives as per usual.
If you can't use Target Disk Mode, you can download DBAN and burn it to a DVD. Boot up using the DVD and you'll be presented with a multitude of options for wiping the drive.
Extract the Hard Drive
The last resort is to open up the Mac and extract the hard drive. You can then use a SATA dock or enclosure to attach it to another computer and wipe it using the tools available (Disk Utility on the Mac, or other tools on Windows). With the exception of the MacBook Air and Retina MacBook Pro, all MacBooks have standard 2.5" SATA drives, so any enclosure that takes SATA will be compatible.
Download GParted and boot from cd or usb stick (by holding down the key Option immediately after chime sounds at startup). You can do pretty much anything you want to your drive with GParted.