As sumofallthings said, Sweeney Todd is an anti-hero. The main character of the piece who we are drawn to root for despite their lack of any "heroic" quality.
I think it is far to simple to refer to every killing in the show as "murder."
Wickedgeek, certainly everyone has flaws, but I think there is far more to the judge's villainy than being a pervert. He misuses his power, rapes, and has predatory incestuous desires.
And Anthony "helping Johanna run away" how is that a "bad deed"?
jasonf, Lovett is the one who takes Sweeney's obsession with revenge and warps it for own ends, ultimately causing the deaths of many innocent people and perpetuating many of the subsequent events.
Although it is very difficult to argue that anyone other than Judge Turpin is THE VILLAIN.
The show is interested in exploring obsession and desire and the depths to which we will sink to fulfill those desires. Every character is effected in some way by their own obsessions.
Even Anthony is not free from this, I have never seen his obsession with Johanna as "pure."
I stand corrected, you are as vapid as they say.