Walk-behind rotary lawnmowers can handle clippings in one of three ways: they can mulch them, bag them or discharge them to the side. Some mowers can do any of the three with minimal adjustment. Any of the three modes can be useful in some situations.

Mulching
For many years, mulching (Figure 1) has received the best "press." Mulching involves holding the clippings under the deck longer so they can be cut multiple times into small pieces and then discharging them directly down. The two primary advantages of mulching (compared with bagging) are the elimination of bags of clippings to be disposed of and recycling of nutrients, primarily nitrogen.
 
The main advantage of mulching compared with side discharge is that mulching chops the clippings and blows them down into the grass instead of leaving them on the surface. Mulching generally requires more horsepower than the other modes since the clippings must be cut multiple times. Mulching works best with dry grass that is not too tall; tall, wet grass will readily plug the mower.
 
Some mulching mowers use a special blade that holds the clippings in suspension longer and recuts them more effectively.

Bagging
Bagging of clippings has been popular for many years (Figure 2). Depending on the model, the collection bag can be mounted on the rear or the side of the mower. The advantages of bagging are mainly visual: The clippings are removed and out of sight. The disadvantages of bagging are the extra work required to empty the bag and dispose of the clippings and the problem of clippings in landfills (if you don’t compost them).
 
Bagging is probably not a good routine practice, but it might be useful if the turf gets ahead of you and is too tall or if you need to cut the turf shorter than usual (before dethatching, for instance). Bagging does put extra stress on the mower because of the weight of the clippings. With some self-propelled mowers, the propulsion system is not adequate to handle the extra weight, and you must help push the mower by hand when bagging. Probably the best use of bagging is shredding and collecting leaves in the fall.

Side Discharge
The oldest way of handling rotary mower clippings is to discharge them out to the side (Figure 3). This system is simple, cheap, requires the least power and puts the least load on the mower. A properly designed side discharge deck will throw dry clippings from a normal cut out to the side and distribute them so that they are barely noticeable. If the grass is wet or very tall, the discharge may partially plug and spurt out unattractive clumps of clippings. Also, not all discharge decks are properly designed; some will not distribute clippings evenly under the best of conditions.

Some mowers are designed specifically for one mode of operation; others can handle two or even all three modes with minor adjustments and attachments. For many people, a side discharge deck will be the most attractive (and lowest cost) option.
 
If you really want to optimize the appearance of your lawn and hide the clippings, consider a more expensive mulching mower. You generally should not plan to bag all clippings, but having the option of bagging occasionally, as noted, might be a consideration. Buy a mower that does a good job of side discharging and/or mulching, and consider ability to bag as a possible accessory.