Back in One Piece Chapter 1047, "The Sky Over the Capital," Kaidō made the bold claim that Haki could transcend everything, including Devil Fruit abilities. To back his claim, he cited how Gol D. Roger became King of the Pirates without ever eating a Devil Fruit. From what's been seen throughout the series, he might be right.
There are several instances of Haki being used to attack and defend against Devil Fruit users. Some have even been shown completely overcoming the more abstract abilities after they've already taken effect. From what's been shown, there should be several more Devil Fruit powers, both seen and unseen, that can theoretically be beaten with Haki.
A common application of Armament Haki is attacking Logia Devil Fruit users. Normally, Logia users' amorphous bodies are immune to physical attacks. However, Armament Haki bypasses this intangibility and allows the user to strike the opponent anyway. It can even be used to attack Logia users whose bodies are made of a dangerous substance like Caesar Clown's toxic gas. With Armament Haki, changing one's form just makes one a bigger target.
Even if a Devil Fruit makes a user dangerous to touch, one can project their Haki outwards to attack the target anyway. Luffy demonstrated this when he punched Kaidō after the Emperor set himself on fire. The Straw Hat captain might also be able to do this if he goes up against Akainu again in the future. Since his attacks no longer require physical contact, he can technically punch anybody.
Armament Haki can also be used against other types of Devil Fruit Users who would normally be able to minimize direct attack damage. This has been shown numerous times with Luffy's Gum-Gum Fruit, but it should also work against Alvida's Slip-Slip Fruit and Jozu's Twinkle-Twinkle Fruit. However a Devil Fruit may improve the user's defenses, a Haki user can attack them through those defenses.
Speaking of defenses, a strong enough Haki user can also ward off the influences of a Devil Fruit power used on them. This ability was first established during the Worst Generation's battle with the Emperors on Onigashima; Law couldn't use his Op-Op powers to teleport Kaidō or Big Mom into the sea because of their overwhelming Haki. Besides the Op-Op Fruit, there are several Devil Fruits that can have abstract effects on the opponent. Fruits like Foxy's Slow-Slow Fruit, Bartholomew Kuma's Paw-Paw Fruit, and Giolla's Art-Art Fruit all employ abilities that directly influence a target's state of being. As such, their powers can theoretically be defended against with enough Haki.
Haki can similarly be used to overcome the effects of a Devil Fruit that have already taken hold. In Chapter 1063, "My Only Family," Law Demonstrated what he learned from the Emperors to overcome a disease of Doc Q's Sick-Sick Fruit. This wasn't just something simple like a cough, either; the Feminization Disease restructured Law's anatomy and turned him into a woman. That Haki could be used to undo such a dramatic change shows the usefulness of the technique. It also shows how much of what a Devil Fruit does is because of the ability itself rather than adverse effects. The more these effects are a result of the Devil Fruit, the more likely that it can be overcome with Haki.
As with nullifying a Devil Fruit, undoing a Fruit's influence to this degree must have several more applications. Besides beating the Sick-Sick Fruit, it might similarly be able to undo the effects of Magellan's Venom-Venom Fruit and Emporio Ivankov's Horm-Horm Fruit. If a person can have their entire anatomy restructured by a Devil Fruit and still expel its influences, they must be able to do the same with abilities that have less dramatic effects.
Of course, this nullification assumes that Devil Fruit haven't taken too much of a toll on them. For example, if someone were turned partially to stone by Boa Hancock's Love-Love Fruit, they might be able to undo that. However, those turned completely to stone would lose consciousness and cognitive function; at that point, they probably couldn't change themselves back no matter how much Haki they had. Thus, similar Fruits to watch out for would be Sugar's Hobby-Hobby Fruit, Charlotte Smoothie's Wring-Wring Fruit, and Tsuru's Wash-Wash Fruit. Haki users' best defense against these kinds of abilities would be preventing them from taking effect in the first place.
If a person has advanced Haki control, anything is possible. This technique gives them the means to deal with any kind of Devil Fruit power both offensively and defensively. Even if those powers are something absurd that warp reality and defy logic, strong enough Haki user can overcome it. In these regards, Kaidō was right to say that Haki transcends all.