What you are referring to is often called "Cross Training" and playing two or three different sports often complement each other because they will keep your senses sharp, contribute to hand eye coordination, increase stamina through activity. There are quite a few articles written on just this topic and I would suggest discovering your local Library to research this further.
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Overall fitness. The main things you should focus on is core muscle hand eye coordination and endurance. But this all depends on what sports your playing.
Power from both the legs and shoulders/arms. Agility is very important. Flexibility is also useful in order to dive for the ball if need be.