Here's a primer on the different kinds of spin and how they affect the ball.

Topspin: This is the most commonly used spin. Topspin is achieved with a low-to-high swing, with the racquet starting below the intended point of impact. The effect is similar to a ball rolling across the floor.
Benefit: Topspin causes the ball to drop as it travels through the air, allowing you to hit safely over the net and still keep the ball in the court.
Who uses topspin: Virtually every player in professional tennis today hits with topspin.

Underspin: The opposite of topspin, underspin (or backspin) is produced with a high-to-low swing and is most often used for defensive one-handed backhands and drop shots.
Benefit: In contrast to topspin, underspin tends to make the ball rise and stay in the air longer, but it can also produce a skidding bounce on shots with a low trajectory. It can cause well-struck drop shots to bounce backward toward the net.
Who uses underspin: Although many underspin shots (except for drop shots) are hit defensively, players such as Tim Henman and Justine Henin can strike underspin backhands that are aggressive. While no top player hits underspin forehands with any frequency, you will occasionally see players use a squash-style underspin forehand when pulled wide, especially on clay. Martina Hingis and Lleyton Hewitt use this shot effectively.

Sidespin: The least used type of spin, sidespin is typically produced when an additional sideways movement of the racquet is added to a player's normal topspin or underspin stroke.
Benefit: Sidespin helps pull the ball wide so your opponent has more trouble reaching it.
Who uses sidespin: Juan Carlos Ferrero sometimes adds sidespin to his forehand down-the-line passing shots; they appear to be going wide and then curl back into the court. It's simply a topspin forehand with sidespin. On the backhand side, Pete Sampras often adds sidespin to his underspin approach as he comes to the net, causing the ball to take a low, sideways bounce.

Slice: A potentially confusing term, slice isn't really a kind of spin, but instead refers to a type of shot. For example, slice can be underspin, as in "slice backhand." Or it can be sidespin, as in "slice serve."

Flat: A flat shot has very little spin. Amy Frazier hits an old-style flat ground stroke. Jimmy Connors is one of the more recent examples of a player who relied primarily on ground strokes with no discernible spin. Although players such as Marat Safin and Monica Seles are said to hit flat, this is true only in comparison to most other professionals. In fact, they both use moderate topspin.

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