You can place plants closer together in a raised bed because you don't need room to walk.  This increases productivity per square foot and reduces weed growth as the plants mature. 

Raised bed gardens allow you to do most of your gardening from the garden path, allowing for reduced soil compaction.  This gives plant roots more access to the air they need.

The raised beds provide better drainage, which also helps plant roots breath.

You can achieve higher quality, richer soil.  You can also  vary the types of soil in different beds.  

Raised beds minimize the waste of water, fertilizer, compost and mulch because you are targeting a very specific area.

Recent studies have shown that raised bed gardens produce 1.5 to 2 times as many flowers and vegetables as regular beds, because of all of the advantages listed above .