One of the most important things that distinguish top players from others is the depth of their shots. There are times when you want to keep the ball short on the table - short serves and pushes (to stop opponents from looping), short blocks (as a change of pace), and wide-angle shots (allowing you to go outside the corners for extreme angles). Counterloops often don't go deep on the table - it's hard to control depth from way off the table. However, these are the exceptions. In most cases you want most of your shots to go deep on the table - pushes, blocks, counter-hits, drives, loops, chops, fishes, and lobs. You also want your deep serves to go truly deep.
By going deep you give yourself time to react to the opponent's shot. You take away the extreme angles, and so have less table to cover. Finally, balls that land in the middle of the table (depth-wise) are easier to attack. Most intermediate players can loop kill or smash them, and advanced players rip these balls with ease. By going deep you make it difficult for your opponent to hit winners or even to play aggressive.
When you see advanced players returning shot after shot, usually it's not that they have incredible reflexes; it's that they are keeping the ball deep, and so can react to the opponent's shots. Weaker players usually put their shots shorter and are unable to react to their opponent's shots, and mistakenly blame it on slower reflexes. (They also place the ball well, usually to wide corners, forcing the opponent to move.)
How does one go about learning depth control?
First, be aware of the depth of your shots. If I catch a ball in the middle of a rally and ask my opponent where his last shot was, he'll usually know the direction but will often have no clue about the depth. Depth awareness often doesn't really come about for many players until they approach the advanced levels - and this lack of awareness often stops players from reaching those levels.
Second, strive to keep the ball deep on most shots, both in games and practice. Stop playing safe, middle-of-the-table shots that are effective against weaker players but are meatballs for stronger ones. Aim for the last 18 inches or so of the table, and you'll develop the habit of keeping the ball deep - and the average level of your opponents' shots will go down dramatically. (Keep in mind that the goal isn't to hit the ball 18 inches from the end-line; it's to hit the ball within 18 inches of the end-line. So your average shot might actually be within a foot of the end-line.)
Third, practice your depth shots. Once they are past the beginning levels most players stop thinking about simple drills like forehand to forehand and backhand to backhand - but it is simple drills like these where you can learn depth control. Put a string or some other marker across the table, about 18 inches from the end-line, and see if you consistently keep the ball past it. Don't try to consciously guide the shot; learn the feel for keeping the ball deep, and let your subconscious take over, just as it should for all learned shots. Perhaps have one player block while the other attacks, and both try to keep the ball deep.
You can practice this on your own with a box of balls. Bounce them on your side of the table and hit to the far side with various shots, and learn the feel for keeping the ball deep. You can practice depth on pushes, drives, and loops in this way. Perhaps put a box against the end-line on the far side and see if you can fill the box up with balls. It's not exactly the same as normally you are hitting against an incoming ball, but it's close enough to practice getting the feel for depth.
You should similarly practice the depth on your long serves. If your serve isn't supposed to go short (so given the chance the second bounce would be on the table or at most barely long - a "half-long" serve), then you want the first bounce to be very deep, within 6-12 inches of the end-line. You have complete control of your serves, so you should have even greater depth control with them than with rallying shots.
Keep the ball deep and your level will leap!