I do both, actually I don't have a lawn but a country yard.
Most of the time I let my grass grow very tall, when I cut I collect the clippings for mulch for my garden or for fodder for my compost.
If you don't allow your grass to grow too tall and you cut on a regular basis it's best to leave the clippings, as long as they are not too thick and matting they will break down and provide valuable nutrients for your lawn.