hmmm..its hard to suggest non-violent MMO's since most [if not all] has their afir share of violence...be it minimal or over the top..
buut, i do suggest:
Uncharted Waters Online - its a sea-faring rpg, its not that violent..sea battles are actually fun once you get the hang of it..
Cosmic Break - a mecha shooter, fast paced and fun to play with friends..
The GazettE ~ I'll show you what Distress means...