Have a look at the different types of sports and some of the examples.
Physical sports – Under physical sports, there is archery, air sports like hand gliding, parachuting, ballooning, bowling, mountain climbing, rope climbing, relay, marathon, hurdles, fast walking, jumping like long jump, high jump, discus throwing, javelin shot put, weightlifting etc.

Cycle and motor sports – This is inclusive of formula racing, kart racing, dirt track racing cycling like BMX freestyle, BMX racing, road bicycle racing, grand prix motorcycle racing, MotoGP racing etc.

Water sports – Wakeboarding, surfing, snowboarding, kayaking, canoeing, boat racing, rafting, rowing, sailing, water skiing, windsurfing, water polo, swimming which includes freestyle, breaststroke, butterfly stroke.

Combat sports – Under combat sports, there is sumo wrestling, judo, wrestling. Combat sports with weapons include fencing, kung fu, sword fighting. Striking sports includes boxing, kickboxing, taekwondo, karate.

Cue sports – Carom, billiards, snooker and pool games all come under cue sports.

Dance – Dance forms are also considered sports. This includes ballroom, salsa, tango, flamenco, lyrical hip-hop, jazz and the likes.

Animal sports – This includes horse racing, fishing, horse polo, elephant polo. Under animal sports, there is cock fighting, bull fighting, dog racing etc.

Ball games – This includes football, soccer, rugby, handball, water polo, hockey which also includes ice hockey, basketball, cricket, baseball, netball, volleyball etc.

Gymnastics – Vaulting, bar gymnastics, group gymnastics, trampoline jumping are all different forms of gymnastics.

Other games – Other games include kho-kho, kabaddi, hide and seek, sac race, lemon and spoon race.

Racquet sports – This includes table tennis, squash, tennis, badminton.

Mind sports – Card games like rummy, bridge, board games like mahjong, Chinese checkers, snakes and ladders are all mind games.

There are several forms of each type of sport. For e.g. in cricket, you have the T20, one-day international and the test format.