The answer is many and varied. Some sports have been played for ever (it seems) and other sports come and go. Some sports are also just for leisure rather than to be competitive. The more common sports played are-
Football -- soccer, rugby union, rugby league, touch rugby and Aussie Rules.
Other ball sports are cricket, field hockey, tennis, table tennis, badminton, squash, softball, lawn bowls, golf, netball and basketball. Indoor cricket and indoor hockey have been played on occasions.
Shooting has been heavily sidelined due to restrictions on the supply of ammunition and equipment but archery has taken a step forward and is gaining in popularity.
Once rallying and speedway were at the forefront in motor sports but rallying seems to have died a slow agonising death due to security issues and it would appear the speedway no longer meets. Go Karts, once the domain of the Moitaka speedway track, was resurrected at the PNG Defence Force Air Squadron hanger but might now be found roaring around the POM Country Club (Old Cathay Club) in Port Moresby, however sports do come and go with the moving expatriate population especially the expensive ones.
Triathlon had a following for a while but the bikes have disappeared off the streets. (See Iron Man article below)
Swimming is ever active with PNG weather making this an ideal way to exercise and cool off at the same time.
People can still be found playing polo, darts, snooker, and eight ball.
Weightlifting has had some interest shown in it after Dika Toua's golden efforts in recent times. Boxing and martial arts, especially karate, kickboxing also has a following in PNG.
Windsurfing was once popular and many sails could be seen off Ela Beach but I think the sport has died completely. Surfing occasionally has an interest with people coming from overseas to surf on the north coast of the mainland. Canoe racing and yachting holds particular interest in Port Moresby. Although the World Sea Kayaking titles were held in Manus a while ago kayaking does not seem to have any following in the country. With so much water around the country Sports fishing is very popular.
Road running holds regular meets but nothing can beat the effort by Tau John Tokwepota, the Trobriand Iron man, in the 1980 Port Moresby Marathon. Tau John was ready to set off for the start of the marathon by car when his car would not start so the only thing was to do a 5 kilometre warm up jog to get to the start passing his rivals already running the marathon on his way to the official start. He eventually started five minutes and 18 seconds behind the leaders and at the first lap had worked his way up to eighth place. Halfway through the second lap he eased his way into third place about 400 metres behind the leaders. He eventually passed the early leaders and won the race 68 seconds in front of the second place getter. Unfortunately Tau John was attacked by unknown assailants years later and his running career ended but his 1980 run surely must go down as being some sort of record.
Talking about road running there are athletic meetings but no junior program to foster the sport. Hash House Harriers meet at various locations around the country usually on a Monday evening straight after work to run their little hearts out.
My apologies to any sport not mentioned above. Perhaps you could write and let me know the ones I have left out. I have deliberately left out PMV drag racing and taxi dodgem from the list of sports. I am still considering whether pothole, zig-zag racing should be included as a sport for most residents of major towns.
Obvioulsy snow skiing is out and I haven't seen any water skiers for a while either but they may still be seen occassionally You can sometimes see kite surfing as well off Ela Beach - as I said the sports played in PNG are many and varied.