I'd argue that the best example is Jiffy Mix, which spends literally no money on advertising, even in the form of the implicit advertising fees paid to direct marketing affiliates. They just put their product on a shelf and people buy it.
We'd expect to see this no-advertising strategy more often in industries where advertising has a significant impact on the cost of the product, and where consumers are very price-sensitive. As Jiffy is very nearly a commodity good, this holds.
In Zara's case, it's "fast-fashion", a segment of the fashion industry where the goal is to provide popular styles of clothing (so product differentiation, a major goal of advertising, does not apply), at low cost (they're targeting price-sensitive consumers), so this strategy is in some sense not a surprise.