The topic of flats vs. clips is a polarizing one, and you'll hear fans from both camps passionately defend their stance. Many new riders prefer to use flats at first, but flats can be good for all levels of riders to properly learn certain techniques like bunny hopping (start video at 10:50), to learn how to keep feet connected to the bike and work on skills that can be scary. Flat pedals are also a great tool for riders of all skill levels to work on riding smoothly, and learning to pump and flow with the terrain to help keep feet on the pedals. This is a technique that can improve your riding no matter which pedals you prefer.
Clipless pedals can offer some power and efficiency advantage when climbing, and some maneuvers are easier to execute while clipped in.
Riding style can also influence pedal selection. Some riders are simply more comfortable on flats for downhill or bike park riding, but may use clipless pedals for less aggressive trail or XC riding. And even some of the most devout clipless riders make the switch to flats occasionally to work on skills. It's all a matter of personal preference, and one pedal style is not superior to the other.
If you're currently riding flats and are clipless curious, consider practicing clipping in and out at least 200 times while riding in a park on grass. Set your Shimano pedals to the lowest tension or use early release cleats with Crankbrothers' clipless pedals. Then, practice on fire road and easier trails until the motion becomes fluid and habitual before riding more difficult terrain. Be patient, and know that when you come to a stop, forget you're clipped in and topple over, this means you're getting comfortable and are almost there!
If you want to try flat pedals, choose a good sticky rubber shoe and grippy pedal, and remember, there is a learning curve here as well. You'll need to spend time smoothing out your pedal stroke if you're accustomed to pulling up while clipped in, and to help keep your foot on the pedal in technical or rough terrain, think about grounding your foot on the pedal and focus on dropping and digging your heels in while descending (this is a good skill to develop regardless of which pedals you ride).