If you own a business sometimes leasing can be a better deal than purchasing. A portion of the lease may be able to be discounted off of your taxes, this may make sense if you need a specialized vehicle or you drive a significant amount of time for business purposes.

If you want to have a car that you'll know you'll need for the long term, you should buy. If you want the coolest, newest car right now and want to trade it in for a newer, cooler car in three years, then take the lease.

However, if you are looking at a lease, know that you're locked into it for the term of the lease, whereas if you buy a car outright you can sell it at any point. Don't make the same mistake I did! See my shared wisdom: Link

If you plan on driving a car past 60,000 miles or so, you should buy. Cost per mile is virtually free,
versus a lease, after that.

When you lease a car, you are basically "renting" it from the company that owns the vehicle and you use it until the end of the terms. When you buy...well it's yours.
With leasing a car, you don't have to worry about trying to re-sell it and be concerning with depreciation of the vehicle as you would if you owned and wanted to sell down the road.
Although when you lease, if there are damages to the car that aren't included in the terms, you would pay extra.
It all depends on what your goals are.