Ideally, services like theirs would be continuously audited by respectable, trusted organizations like the EFF.. multiple such organizations even.
Then I'd have at least some reason to believe their claims of not collecting data about me.
As it stands, I only have their word for it.. which in this day and age is pretty worthless.
That said, I'd still much rather use DDG, who at least pay lip service to privacy, than sites like Google or Facebook, who are openly contemptuous of it.
At the very least it sends a message to these organizations that privacy is still valued, and they'd lose out by not trying to accommodate the privacy needs of their users to some extent.