The most common causes of steering looseness include worn tie rod ends, a worn idler arm or center link (on vehicles without rack and pinion steering), a worn steering gear or a worn steering rack.
Normally, your steering wheel should have no more than about a quarter inch of play. Any more means something is worn or loose and needs to be fixed.
The inner and outer tie rod ends should have no perceptible looseness. Worn or loose tie rod ends are especially dangerous because if one pulls apart you'll lose steering control. Worn tie rod ends can also cause rapid tire wear.
If you have a rear-wheel drive vehicle with conventional steering (not rack and pinion steering), the idler arm should have no more than the specified amount of maximum play. Refer to a manual for the specs and recommended procedure for checking it. Checking idler arm play usually involves pulling on the arm with a specified force and measuring how much the arm deflects.
If your vehicle has a lot of miles on it, the steering gear or rack itself may be worn. On conventional steering boxes, there's usually an adjustment screw that can be used to take some of the slack out of the system. With rack and pinion steering, though, adjustment is usually little help because the rack develops center wear. If the pinion is adjusted to compensate, the rack may bind when turned to either side. The only cure for a center wear condition is to replace the rack with a new one (an entire new rack assembly).
Sometimes the steering will feel loose because of a worn U-joint coupling in the steering column. Loose or worn wheel bearings can also make the steering wander and feel loose.