Since you only pay for the amount the vehicle depreciates while it is in your possession, monthly payments are significantly lower than purchase payments over the same term.
Nicer vehicle every few years:
With lower monthly payments, you can afford a better car. And, since lease terms are generally shorter, you can get these better vehicles more frequently.
Less maintenance headaches
Lease terms generally in the 2436 month range tend to expire around the time new car warranties run out. Hence, by the time the car ages sufficiently to be a maintenance problem, it won't be your problem.
No car disposal nightmares
Most leases put the burden of disposing the used vehicle on the dealer. Therefore, when the lease term is over, if you either don't have, or don't choose to exercise, a purchase option, the car is not your problem.