On ABS-equipped vehicles, all vehicle manufacturers recommend using the same size and aspect ratio tire as the original. ABS systems monitor the rotational speed of the tires through individual wheel speed sensors. Changing to an oversize tire with a taller diameter than stock would cause the tires to rotate at a slightly slower speed relative to vehicle speed than the stock tires. Changing to a low profile tire with a shorter diameter would cause the tires to rotate at a slightly faster speed relative to vehicle speed. Though the difference either way isn't much, it may be enough to upset the calibration of the ABS system and have an adverse effect on its ability to detect and prevent skids.
Another reason for not changing tire sizes is because it can affect the speedometer, odometer and transmission shift points on a vehicle with an electronic automatic. Oversize tires will make your speedometer read slower than normal (which may get you a speeding ticket unless you have the speedometer recalibrated to compensate for the change in tire size!). Smaller diameter tires will make the speedometer read faster than normal, and increase the mileage readings on your odometer at a faster than normal rate.
All this doesn't mean you can't change tire and wheel sizes, however. If you maintain the same overall tire diameter as before, you can switch to larger wheels with a shorter aspect ratio tire. This is the basic idea behind "Plus 1, Plus 2" tire and wheel sizing.
Replacing a stock 14-inch wheel and 70 series tire with a 15-inch 60 series tire would be Plus 1. Plus 2 would be moving up to a 16-inch wheel and possibly a 50 series tire. Plus 3 would be going to the new 17-inch tire and rim combination -- which could turn out to be a Plus 4 application if the vehicle originally had 13-inch wheels.
The "aspect ratio" of a tire is the ratio of its section height to its section width. The smaller the number, the shorter the sidewall and the wider the tire. Low aspect ratio tires started with 60 series some time ago, then progressed to 50 series and now 45, 40 and even 35 series tires.
Shorter aspect ratio tires (60 and less) are usually considered to be performance tires because they lower vehicle ride height, have a wider tread and put more rubber on the road to improve handling. But the shorter the sidewall, the harsher the tire rides.
A tire's ability to support a given load depends on its air volume. If you go to a lower aspect ratio tire with a shorter sidewall, the tire must be wider to maintain the same air volume. If you just go to a shorter aspect ratio tire without increasing width, the load carrying capacity goes down. That's why when you go from a standard wheel to a Plus 1 wheel, the rim is usually wider to accommodate a wider tire.
It's important to follow the tire manufacturer's recommendations as to load capacities when going to larger wheel and tire sizes. There's no hard rule that says you have to drop 10 points in aspect ratio when increasing wheel size one inch, but that's the general recommendation.