Pretty much never. The security gain difference between the two last options is very small, negilgible and only justified if you have some high-value data on the disk being wiped.
The first three options are virtually the same, just fill the disk with a fixed pattern. This is optimal for home users selling the computer for example, or to delete some confidential data you don't want exposed, but that's it, no special procedure is performed, just plain old overwrite.
The fourth option uses a particular US goverment procedure that wipes data and makes extremely difficult to undelete it, even with professional support. It overwrites the data 3 times with different patterns each time to ensure data is unrecoverable.
The last option is an even stricter procedure. In theory it's supposed to be used to wipe top-secret data from government and military servers, maybe from corporate ones too. In practice, it doesn't offers much more protection than the previous method. And even more in practice, if you've got data that could endanger lives/goverments/corporations/whatver seriously if exposed, you shouldn't be wiping the disk, you must physically
destroy it. Plain old brute force. Real life brute force I mean.
Which renders the last option useless to all practical effects.
