Sports are helpful across the board.
Sports develop:

Physical health
Mental health
Confidence
Focus
Fairness
How to follow rules
How to win gracefully
How to deal with losing
Teamwork
Compassion
...all while having fun!
"But what if my kid sucks at sports?"
All the more reason to try! Learning how to improve a weak area is an essential life skill, and there is always room for improvement even if you never go pro.
"Ok but my kid HATES all sports!"
Find the one they hate the least and insist on them doing it...and play it with them if you can.
No, not everyone is meant to strap on pads and play tackle football...but even ping-pong counts!
I gauruntee that there is at least one game in gym that they like...go with it!
Best Sports for kids:
Baseball - Involves boring periods of waiting, but teaches many real-life lessons.
Basketball - High cardio, courts are plentiful, and you just need 1 ball.
Wrestling/Boxing - Great for agressive kids. Yes it is physical, but orderly, controled, and organized.
Martial arts - A good martial arts program is absolutely the best thing for any child. Contrary to belief, martial arts teach you to avoid fighting, and provides a life philosophy of focus and discipline, while providing confidence, self-esteem, and the ability to protect yourself if need be.
Sports with concerns:
Football - Although football teaches teamwork and strategy...it has a higher risk of injury.
Weightlifting - Body building for mass should never begin before the body is done fully growing.
Hockey - Ice/Roller hocky is not particularly dangerous at the youth level, however the equipment is expensive, and you need a lot of it.
There are many other sports that your kid may prefer - gymnastics, soccer, volleyball, track...Let them choose what they want, but put them in SOMETHING!
Summary
Sports are now even more important than ever!
Kids spend more and more time indoors and on their phones than any time in history...and obesity is out of control. Sports are just the way to make up for these times of reduced exercise and let you actually socialize with real people. They provide valuable life lessons...all while having fun!
Joining an organized team sport is ideal. Speak with your school to see your options.