What program do you use to securely delete/wipe/erase data on hard drives?

Darik's Boot and Nuke - "Darik's Boot and Nuke ("DBAN") is a self-contained boot disk that securely wipes the hard disks of most computers. DBAN will automatically and completely delete the contents of any hard disk that it can detect, which makes it an appropriate utility for bulk or emergency data destruction."

The method we use is: "American DoD (Department of Defense) 5220-22.M Standard Wipe Short" - A 3-pass wipe using random characters, complements of characters, and random data streams. (i.e. Writing random characters to the hard drive to erase data and doing this 3 times.)

Can I just format to securely delete/wipe/erase data on a hard drive?

No - This is because formatting a hard drive does not destroy the data on the hard drive it merely marks that area of the hard drive as writable by the Operating System. So the previous data is left there until the Operating System writes/saves new data in that area of the formatted hard drive. Therefore you can most likely recover data from a formatted hard drive.

What is the difference between High-Level formatting and Low-Level formatting?

Low-Level formatting - Mainly done at the hard drive factory and never by a computer user. Low-Level formatting is used to outline areas (tracks and sectors) on the hard drive so physically the hard drive is ready to be used. This type of formating involves the circuit board on the hard drive.

High-Level formatting - This type of formatting we can do as computer users. High-Level formatting is usually done before an Operating System is installed. Also it's done after installing a brand new hard drive. This formatting changes the file system on the hard drive so the Operating System that you use can write and save data to the hard drive.