One of the biggest problems beginning/intermediate players have is standing up too straight. Watch the top players and you'll see how they stay low - feet relatively wide and pointing slightly outward, weight toward the front inside balls of their feet, knees bent, and leaning slightly forward from the waist. This allows much stronger play than standing up straight - you'll move quicker, have better balance, recovery more quickly after shots, and your shots will be more natural and more powerful. And you'll even feel more like an athlete because you'll be playing like one!
Here's a good example - here are highlights of the Men's Singles Final at the 2013 World Championships between Zhang Jike and Wang Hao, both of China. Or pull up just about any video between two top players. It may not be easy to play with a lower stance at first. Older players and those with knee problems might have particular problems, and might need to adjust - but even they should focus on staying at least somewhat low.
Why is staying low important?
Besides table tennis players, you can find examples of athletes staying low in many sports - for example, an infielder in baseball, a goalie in soccer, and basketball players when they are dribbling or covering someone.
You might have to build up your leg strength to stay low - but staying low in itself builds up those muscles, and the more you do it, the stronger your legs will be, and the easier it becomes. Truly serious players should hit the weight room and focus on lower body strength training.
You can make the change to a lower stance in stages, focusing on staying a bit lower for a week, and a bit more the following week, and so on until you find a comfortable low stance. If this doesn't work, try going for the other extreme, and practice staying too low. (Careful if you have knee problems!) It may feel silly, but after playing that way for a short time you may find it easier to compromise between the too-low stance and your previous too-high stance.
And when you develop the habit of staying lower, you'll begin to feel the benefits as your game improves. A lower stance will allow you to stand tall on the winner's podium.