There is drop in ball hockey on Wednesdays and Thursdays from 8:30-10:30pm at the Hintonburg Community Centre. Not sure if it goes all summer or not, but it will definitely be running for the next few weeks. $3.25 per person.
Most, if not all summer leagues have started. I'd suggest contacting Dave (he runs GOBHA) or Al (runs OCBHA) to see if you can get a spot on a team. I think each league has a team comprised of people who just want to play but don't have a team.
You can also try www.ottawaballhockey.com. Less organized, smaller playing surface, no helmets, no slap shots, no icing or offsides...stuff like that. Still fun.