One of the core exercises that every basketball player (that is old enough) should be doing is squats. There are several different squat variations that can be done, but this video is going to cover the front squat exercise. Front squats are going to really help build up the players core strength and also their legs. The core and legs are where a players power and explosiveness come from, so this is very important.
It is not enough to only spend time working on the court to become a better player, because basketball continues to become more and more fast paced and athletic. Along with your on court basketball training there needs to be specific time spent on develop strength, explosiveness, etc. and this is a great basketball exercise to get started with. Make sure though that you really focus on the form and technique for this exercise. Doing it the correct way will make sure that you are getting maximum results, and will also help to prevent injuries.