I wrote earlier of a type of product where tariffs actually make sense - basically, a heavily branded product where there's actually not much of a difference in quality, but a big difference in price.
Another type would be a good with significant negative externalities, like rainforest-derived products. For example, if you have paper, which is produced fairly responsibly in the US and extremely irresponsibly in Brazil, putting a tariff on Brazilian paper increases the price of paper to Americans and reduces the welfare Americans as a whole receive from paper. However, the destruction of the rainforest represents a significant negative externality to the world, and Americans as well.
Rational economic theory states that goods with negative externalities should be subject to Pigouvian taxes. Tariffs on the product functionally then can serve as a partially-Pigouvian tax. On a strictly economic basis (excluding moral or socially responsible issues), you can't have the US put on full Pigouvian taxes, because it sacrifices US welfare for the benefit of everyone else (tragedy of the commons). But you can partially tax it - the welfare we'd lose in paper would be made up for by making it easier to find pharmaceuticals or other things that the rainforest helps us do.
In that sense, this represents another type of good tariff. Not quite as interesting as the other kind, but no less valid, I think.