Virtually all sporting activity can still be actively enjoyed by people with one eye.
Some sports will require a period of re-adjustment from binocular vision to monocular vision like: golf, fishing, football, bike riding and skiing as they all involve depth perception. Sports where there will probably be no real adjustment needed would be: pool and snooker, running, hiking and swimming.
There is one sporting activity you may wish to reconsider as it includes a possibility of injury due to high-speed ball impact, namely that of Squash. A typical squash-ball is just the right size to cause major harm on impact with your remaining eye.
Also it is recommended that swimmers wear goggles to prevent possible displacement of the artificial eye due the forces of water, or socket irritation from Chlorine.