Here are two examples of the general rule that natural selection lets you predict, before seeing it happen, that a population, given some kind of new selection stress, will adapt to it.
In Asia, only male elephants have tusks, but they don't all grow them at the same rate so they don't all get to the same size, and a few are essentially tuskless. Due to human hunting, big tusks have become a disadvantage, making the individual who has them more likely to get shot. It was predicted decades ago that this might be shifting the population toward smaller tusks and/or outright tusklessness in males. Sometime within the last few years, wildlife biologists have confirmed that this is indeed the case: tuskless males are now a larger percentage of the male elephant population, and, among those who have tusks, the average and maximum observed tusk sizes have decreased.
Monsanto wanted to make plants that could survive Roundup (a fast-acting herbicide that works on all plants by blocking photosynthesis but breaks down quickly so it doesn't have time to harm the surrounding environment). This would allow Roundup, a Monsanto product, to be used more widely, replacing various other narrow-spectrum herbicides which tended to remain active longer and thus disturb natural environments more (and which didn't kill 100% of weeds and sometimes could harm some of the crops). But they hadn't invented any kind of Roundup immunity in plants and had no idea how, so they decided to try to find it instead. Natural selection told them where to look: in photosynthesizing bacteria and algae which had been exposed to various concentrations of Roundup, because they were initially affected by it in the same way as plants but could evolve a response to it many times faster than plants could. It worked, and they began inserting the Roundup immunity gene they found into crop species, thus producing crop plants that could be sprayed with Roundup and be unharmed.
Also, Darwin's original book about natural selection contained some predictions based on it which have turned out to be right since then but weren't known at the time. Some were just about the existence of transitional fossils, such as extinct land mammals and semi-aquatic mammals connecting whales & dolphins to the rest of us as descendants of former terrestrial mammals. Another was that if a reliable and precise dating method were invented (since they had no idea what numbers of years to assign to things back then, before radiometric dating!), it would show that the relative ages between certain fossils came in the right order and had enough time between them. Another was that the mechanism for how traits are inherited and yet random variations occur (for natural selection to act on) was to be found in the organisms' chemical constitution, and indeed genetics is a complex application of chemistry. But my favorite one was that, when discussing the fact that large groups of plants seemed to be closely related to others in the wrong places, such as Africa and South America, he pointed out that we don't actually know that the continents have always been where they are now (everyone just assumed it must be so back then, so this was a subtle point of logic)... and that if anything his theory called for them to have moved and merged and split up before in order to yield the current distributions of organisms... which would not be commonly accepted by geologists for roughly a hundred years after he wrote it.
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