What is the most secure method to erase hard drive files?

I just got a program that can "shred" files so they cannot be recovered. It offers 4 erasing methods:

• Random Data Method (1 pass)


• US DoD 5200.22M-STD (3 passes)


• US DoD 5200.28-STD (7 passes)


• Peter Gutmann Method (35 passes)

The program claims that the Gutman algorithm is the most secure, however I've read that that method is not necessary now with modern hard drives (not SSDs) and only a few passes or random scrubbing should be enough.

Which is the most secure method (with out actually having to physically destroy the drive)?