not instead of lawrence's answer but in addition to it:
whether something is violent and whether something is productive depends entirely on how one defines violence, and on what one is trying to produce.
many people on this site both want a dramatically different world/social set up, and have experiences that seem to prove that the tactics that we know and recognize now don't work to create what we want. so if that new world is what we're trying to produce, i can certainly say for myself that i don't know what will be "productive." what i do think, based on my experiences, is that anger is essential, and that aiming that anger at the enemy (sometimes outside myself, and sometimes not) is an important part of rejecting what i don't like about the world. and i have not seen pacifism ever create anything (at least not that i recognized).
there are books you could read - peter gelderloos wrote two books on this, how nonviolence protects the state and a more recent one (can't remember the name), and ward churchill (not an anarchist, but...) wrote a smaller book called pacifism as pathology.
and just so we're clear, there are plenty of anarchists (or, for the sticklers among us, "people who call themselves anarchists") who agree with how you present the question - they accept the definition of violence given to them by the corporate media, they believe that the way to change the world (and people's minds) is through positive programs, and they know that anarchists have a lot to offer in terms of better strategies and tactics and relationships. these people get very excited about things that don't matter to me, and i think they don't understand some important things about what they're talking about (like moral purity, as lawrence mentions), but those might be topics that you have to experience yourself before we can have a good conversation about them. (or at least that would be a different question, with its own thread.)