Research shows it's best to replace all four tires at once, but if you can only afford two, which wheels should they go on -- front or rear?

If only two tires are installed, whether they are all-season, winter or rain tires, research indicates its safest to put them on the rear position, as this gives the best lateral control, especially in corners. This fact holds true for all vehicles, including rear-wheel drive, front-wheel drive and four-wheel drive models.

Logically, you might think it's best to put them on the front drive wheels of a front-wheel drive car, but that's not the case, as it's safer to have increased lateral grip on the rear. You can usually regain control of slipping front tires by lifting off the accelerator, but if the rear end breaks loose, you're in for a spin and possibly a crash.

The rear tires of any vehicle must have comparable or higher traction capabilities than the front tires in order to optimize vehicle mobility and control, especially during sudden manoeuvres, according to Cooper Tires.

Cooper states: "If winter/snow tires are applied to the front axle of any vehicle, winter/snow tires must also be installed on the rear axle. DO NOT apply winter/snow tires only to the front axle. This applies to all passenger and light truck vehicles including front-wheel-drive, 4WD, and AWD vehicles. WARNING! Without winter/snow tires on the rear axle, which have comparable traction qualities to the tires on the front axle, the vehicle may experience adverse handling characteristics. This may result in loss of vehicle control, which could cause serious injury or death."

Most vehicles are equipped with the same size tire at every wheel position. Ideally all of these tires should also be of the same type and design, have the same tread depth and be inflated to the pressures specified by the vehicle placard or owner's manual. This combination best retains the handling balance engineered into the vehicle by its manufacturer.
However due to a front-wheel drive vehicle’s front tires' responsibility for transmitting acceleration, steering and most of the braking forces, it's normal for them to wear faster than rear tires. Therefore if the tires aren't rotated on a regular basis, tires will typically wear out in pairs rather than in sets. And if the tires aren't rotated at all, it's likely that the rear tires will still have about 1/2 of their original tread depth remaining when the front tires are completely worn out.
Intuition suggests that since the front tires wore out first and because there is still about half of the tread remaining on the rear tires, the new tires should be installed on the front axle. This will provide more wet and wintry traction; and by the time the front tires have worn out for the second time, the rear tires will be worn out, too. However in this case, intuition isn't right...and following it can be downright dangerous.
When tires are replaced in pairs in situations like these, the new tires should always be installed on the rear axle and the partially worn tires moved to the front. New tires on the rear axle help the driver more easily maintain control on wet roads since deeper treaded tires are better at resisting hydroplaning.
Hydroplaning occurs when the tire cannot process enough water through its tread design to maintain effective contact with the road. In moderate to heavy rain, water can pool up in road ruts, depressions and pockets adjacent to pavement expansion joints. At higher speeds, the standing water often found in these pools challenges a tire's ability to resist hydroplaning.
Exactly when hydroplaning occurs is the result of a combination of elements including water depth, vehicle weight and speed, as well as tire size, air pressure, tread design and tread depth. A lightweight vehicle with wide, worn, underinflated tires in a heavy downpour will hydroplane at lower speeds than a heavyweight vehicle equipped with new, narrow, properly inflated tires in drizzling rain.
If the front tires have significantly less tread depth than the rear tires, the front tires will begin to hydroplane and lose traction on wet roads before the rear tires. While this will cause the vehicle to understeer (the vehicle wants to continue driving straight ahead), understeer is relatively easy to control because releasing the gas pedal will slow the vehicle and help the driver maintain control.
However, if the front tires have significantly more tread depth than the rear tires, the rear tires will begin to hydroplane and lose traction on wet roads before the fronts. This will cause the vehicle to oversteer (the vehicle will want to spin). Oversteer is far more difficult to control and in addition to the initial distress felt when the rear of the car starts sliding, quickly releasing the gas pedal in an attempt to slow down may actually make it more difficult for the driver to regain control, possibly causing a complete spinout.