I have read I should leave my grass clipping on my lawn after I mow. I have always bagged.
Master Gardeners do not recommend catching grass clippings during mowing. You are actually depriving your lawn of valuable nutrients when you do. We recommend that you use a mulching mower or mow more frequently instead. A mulching mower has the grass discharge blocked so the clippings stay around the blade longer and are chopped up into smaller pieces. They settle down between the blades of grass and do not detract from the appearance of the turf. Leaving clipping will save you money as you will find your lawn will need less fertilizer. The grass you return to your lawn is full of nitrogen and other trace minerals the grass needs to be healthy.
If you have a lot of grass clippings, we would recommend that you start a compost pile. Included are a few of links on composting to help you begin the process.