People who take antidepressants are more depressed than people who do not. If we just look at the correlation, we might assume that antidepressants cause depression, but the opposite is true.

In this case, there's still a correlation, but the sign is the opposite of the true causal effect of taking antidepressants.

Alternatively, consider a car being driven over a hilly road at a constant speed. When the car is going uphill, it's burning more gas. There's no correlation between speed and gas consumption, but gas consumption increases speed.