Hello and thank you for contacting us. This is Dwayne B. and I’m an expert here and looking forward to assisting you today. If at any point any of my answers aren’t clear please don’t hesitate to ask for clarification. Also, I can only answer the questions you specifically ask and based on the facts that you give so please be sure that you ask the questions you want to ask and provide all necessary facts.
Generally, lawsuit for this type of thing haven't been effective other than to recover a ring, any costs associated with the wedding planning (ex. deposits to reserve a hall, etc)
There have been a few lawsuits (you can read about one at http://www.today.com/id/47540442/ns/today-today_news/t/man-sues-ex-fiance-after-she-breaks-engagement/#.Vr_ENPkrJpg) when someone has incurred other expenses associated with an engagement.
So, if that's what you're talking about then yes, a lawsuit is possible. Likewise, if you quit a job to move somewhere else based on the promise to marry then it is possible you could sue to recover damages associated with that.
However, just suing in general for breaking up or breaking off the engagement without any specific damages wouldn't likely be a viable case. A lawyer would charge you a lot ot take the case and you wouldn't be likely to succeed and recover much, you'd be more likely to spend more than you would recover.