On a personal level, it all depends on your skill.
As a comparison, the fastest a professional has hit a forehand was 120 mph (by Gael Monfils), and 155 mph on a serve (by Andy Roddick).
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The ball itself can travel as fast as a force exerted on it can send it. This can range from 1 mph to 1,000 mph.
An average first serve speed for male professional tennis players is about 120 mph, but it has been observed to be as fast as 155 mph (Andy Roddick, USA). Likewise, a male professional player's second serve speed can vary, but it is on average about 92 mph.
An average male professional tennis player's shot speed is about 70 mph, with fast-paced winners increasing to speeds up to 110 mph (although it can be higher on rare occasions).
Obviously, each shot can vary in speed depending on the kind of shot being hit, the speed of the ball before it makes contact with the racquet (depending on whether the shot is a return of the opponent's shot or not), whether the player is male or female, the player's age, the player's experience, and the player's physique.
Reiterating the basic answer to the original question, there is no limit to the speed a tennis ball can travel.
The speed of the ball can vary from slow serves with much spin to smashes that travel as fast as 112.5 kilometers per hour (70 mph).