You have front and rear swaybars. They help control body roll.
Thicker swaybars keep the car more level in a corner, softer ones allow for body roll.
If your front swaybar is too thick, you can induce inner wheel lift in a corner, as well as understeer. If your rear swaybar is too thick, you can suffer from premature oversteer.
Aftermarket swaybars can be thicker, thinner, adjustable - just about anything you want. They're a good way to make your car handle firmly through corners without having to run hard springs, which most people to do compensate.
To get the best balance, it's important that the sway bars, springs and shocks complement each other (and that doesn't mean talking to each other every morning saying how nice they look).
If your front sway bars are too heavy for the spring settings, as already mentioned, you will end up with a car that handles like a dog, understeering like buggery. ( I know, I did it on my HR). You will find that there is usually more than one diameter sway bar from the factory for each model (ie 6's have one setting, 8's another, utes another etc.) because of the differing body weights and spring/shock settings. Just as an example, the early 6 and 8 cylinder Commodores had front and rear bars, the 4 cylinders didn't have the rear.
They're certainly not a last option - rather, they are a very vital component.
sway bars can be used to "tune" the suspension .i.e. for under/oversteer as morton mentioned. get it right and the car will handle like it's on rails, get it wrong and you could findyourself wrapped around a tree.
generally, from factory, cars are setup with understeer. it's safer. in a understeer condition basically whats happening is that you turn the wheel but the car plows on straight ahead, basically the front tyres don't have enough traction. the best solution in this situation is to reduce speed and allow the tyres to gain traction. seeing as the majority of the driving public hit the brakes when something goes wrong it's the safest way to setup a cars suspension.
the same reason why front wheel drive cars are also safer. loose traction because your giving it to much gas and the car will just go straight ahead, take foot of gas and apply brakes and you regain control and are probably still going in the same direction as intended.
with a rearwheel drive car thats setup for oversteer, loose traction through a corner and you find you'll be looking at the cop thats following you as you slide of the road heading for that tree you were looking at 2 seconds ago