Aside from the random fluke injury (catch a toe, swept over ankle wrong, post wrong / hand slip, etc) how you train and who you train with are going to be the biggest factors in if you get hurt or not.
Going hard with spazzy white belts (until you are good enough to control them) = injury
Hard, competition style rolling, while enjoyable, does increase the chance of injury.
Playing a ton of closed guard, rubber guard or letting yourself get stacked = injury.
And obviously, not tapping when your caught = injury.
It's a contact sport, so expect a # of bumps bruises and soreness. But if you are training 2-3 times a week, are fairly good, tap when you should and avoid being stacked a ton - you should be able to roll pretty hard most of the time and avoid major injury.