When breaking up you should always make an attempt at civility. Although, as you can see above, this is not always possible. Therefore, you should take several steps to ensure that you are not the one that steps out of bounds.
First, think about how you are going to perform the break up at least a day in advance. If you fail to plan, you are planning to fail.
Next, refine your reasons for the breakup. Make it appear as though you are doing this because of something that was your fault, whether it is or not. This way the breakee can save face, a small price to pay to avoid having a bitter enemy for life.
Finally, make it quick. Get in and get out. The longer you stand around discussing what could have been, what should be, and how things might turn out, the more likely the breakee is to start throwing out landmine remarks and hurtful jabs. Give them time to cool off, then call and ask them to join you in a platonic activity. If you manage to contact them directly, excuses will probably not be in short supply. If you have to leave a message, chances are they will ignore you and not return your call. Either way, the ball is in his/her court and you have done your best to stay friends. Voila! You can now forget about them and move on.