Certainly not all correlations are useless. This feels like I am breaking some analogue of Godwin's law, but just consider the association between cigarette smoke and some types of cancer. Generally, discounting correlations and treating them with more skepticism seem like good ideas. But "throwing out" seems needlessly harsh to me, unless for some reason you are in a hurry, in which case you should think about deferring to more expert sources anyways.

For example, this useful source http://www.informationisbeautiful.net/play/snake-oil-supplements/ (see the spreadsheet at the link) uses mostly randomized trials but also includes some studies which discuss prospective associations. I don't think the organizers should be criticized for including the correlations.