There sure is, there's numerous leagues out there that are run by players, www.myleague.com is a major site I believe, but check around in league rooms to see if anyone is advertising their league to join.
Also there's official tournies run by the site, for both subscribed and non-subscribed players.
http://www.flyordie.com/games/tournamentSchedule/?lang=en&game=Snooker&portal=flyordie_com
That's just tournaments for snooker however there are some for 8 ball and 9 ball. ;)
In addition to all this there are a few forum tournaments popping up (-Paralyzed- is currently running one and a guy called Championship did one a few weeks back) so keep checking the forum regularly to see if anyone's thinking of starting a tournament. :)
Hope that answered your question. :p