There is the #1 safety break used by a lot of players which AZE described.
I have also seen advanced skill level players break to pocket a ball on the break. I heard a new player in our area can pocket the head ball in the side pocket about 3 out 4 times (75%). And I believe it, because he kicked my arse in 8 ball last week (5 games to 0).
Once, you get the safety break down. I think working on the offensive break during practice would be a good thing. I just wouldn't bring it out during a match, unless I could pocket the ball consistently.
I have also seen another str8 pool player practicing POWER secondary break shots because, as you may already know, using a lot of power in a shot will change the OB's track line.