Tire pressures. Sure, there'll be a tag on the swingarm somewhere, as required, but the manual will also provide recommendations for different loading and speed scenarios as well.
Oil level. Most bikes have a sight gauge, but do you know if the manufacturer specifically recommends checking the level with the engine hot? How about on the centerstand or just held level? And if your bike has a dipstick, do you know if the level is measured with the dipstick just placed into the opening, or with it all the way seated? For that matter, do you know if that warning light is for oil pressure or level? (Yamaha owners are having a chuckle at this.)
Instruments and menus. Today's bikes pack a ton of information into the multifunction displays and often hide functions inside seemingly torturous menu systems. Want to switch off the ABS on your Triumph Tiger 800? Reset the traction control on your MV Agusta? Decipher what the iconographs on your BMW GS are telling you? Better crack the book, bub.
Sometimes simple stuff isn't. For example, Honda's NC700X violates a rule most Hondas adhere to. Specifically, most Hondas use a single button to toggle between the odometer and tripmeter functions; press and hold that button to reset the trip. Not on the NC. Instead, you have to press and hold the other button for a few seconds. But press it too long and you'll end up in another setup menu. At first, we thought our early production NC was busted. Then we read the manual.
Warning lights. Modern bikes are supposed to warn you when something's amiss in the electronics or the emissions-control system; they'll usually do that through a light. Sometimes the sequence of blinks, or a blinking light combined with an error code displayed on the digital instruments will tell you where the problem lies. (The manual will just say, "go see a dealer," but with some research you can get ahead of the curve.) For many error codes, the answer is in the owner's manual, though some manufacturers make you look into the service manual for clues. Either way, you'll never figure it out by guessing.
Suspension adjustments. For sport riders who wander down the dark lane of suspension adjustments, the owner's manual is their pocket full of breadcrumbs. Don't assume you're going to make progress without a good baseline, so always start with what the factory says are the normal settings. We've seen it too often: A rider gets lost in the setup and isn't sure which of the many adjustments turned his sportbike from "not quite right" to "intent to maim." Go back to the stock settings to start over.