Even in a world of superpowered beings, Shazam has more abilities than most. But while flight, superstrength, and the ability to summon magical lightning are powers any hero would covet, the Champion of Eternity possesses one superpower that every hero seems to have, but which is actually canonical for Billy Batson's alter ego.
Empowered by the Wizard, aka Shazam, Billy Batson is able to transform into an adult, superpowered form when he speaks his patron's name. This gives him the wisdom of Solomon, the strength of Hercules, the stamina of Atlas, the power of Zeus, the courage of Achilles, and the speed of Mercury (though different interpretations have juggled these details when convenient.) Each of these attributes actually speaks to several different abilities, but it's the wisdom of Solomon that makes Shazam particularly unique.
The wisdom of Solomon pairs Billy Batson's natural curiosity and empathy with stores of instinctive knowledge. Using his powers, Shazam is able to make leaps in intuition and logical thinking. In Captain Marvel Adventures #137, from Otto Binder and C.C. Beck, it's demonstrated that Shazam is able to connect events in ways he couldn't in mortal form, and later writers have expanded this even further. Shazam is able to speak any language and is even capable of limited precognition, as his powers allow him to piece together educated guesses about the future even if he doesn't quite know how - if Shazam has a hunch, it's worth following. But the best application of this semi-precognition is that Shazam has the uncanny ability to figure out where he needs to be in order to offer help to others - something that Geoff Johns and Gary Frank's New 52 Shazam! run described as, "being drawn to places of need."
Partly due to his magical nature, and partly due to the impeccable judgement provided by the wisdom of Solomon, Shazam has the often overlooked power to instinctively sense where he's needed. The average night out walking around Philadelphia will see Shazam happen across (and thus prevent) random crime after random crime. Of course, this is a superhero's lot in life, but for other vigilantes, it often makes a lot less sense. While heroes like Daredevil and Superman have super-senses that allow them to pick up on cries for help, others such as Batman and Spider-Man happen across criminal acts with surprising frequency, often zeroing in with inexplicable accuracy on the misdeeds that involve their own personal rogues galleries.
In contrast, Shazam happens across those who need his help as part of his powers. Not only does this fix the plot hole of how one individual - even one who goes out on "patrol" - ends up filling their night with crime-fighting, but it means he's able to help even those people who might not be able to call for help or whose need is more mundane. Shazam isn't drawn to conflict but need, and potentially even need that isn't yet apparent. Spider-Man has to get very lucky to save someone from being hit by a car, for instance (though he frequently does so), but for Shazam, the wisdom of Solomon ensures he's in the right place at the right time to help out.
A uniquely optimistic hero, it's entirely appropriate to Shazam's magical roots and childlike ability to act as a paragon of virtue that he possesses the forgotten superpower to intuitively discover those who need his help, whether with a supervillain or because their cat is stuck up a tree.