Hee-hee. The age-old question. Just what is the best way to deliver potentially devastating news? I think the duration and intensity of the relationship that you are ending should be taken into account, as should the level of commitment. You cannot end a marriage via text message, and the same goes for an engagement. If you have only been seeing someone for a few weeks though, you can. It's not a very nice thing to do though.
Don't dwell on the reasons
Face-to-face is the only suitable option for ending long-term relationships or an intense interaction in which you might have created long-term expectations such as marriage etc. Make sure you do this in a public place, or at the other person’s house so that you can exit once you have delivered your hurtful news. Make sure you state what you want clearly. 'I am ending our relationship. It is simply not working for me and I want something different.'
Do not talk too much about your reasons because this might lead to negotiation with your partner saying things like, 'I can change.'
Mobile is cowardly but okay if you do not know this person too well, are not too socially intertwined, and you do not really care what they think of you. If you met them through a friend, co-worker or family member, you have to go with the face-to-face. Again, state your point quickly and get off the phone.
Ultimately, your break-up method says more about you...
Silence is violence
The above two are the only appropriate methods I can think of. Text messages, Facebook, or other chat formats are so cowardly you might as well just shut up and choose silence.
Silence is an all too common method of breaking up. I do, however, believe that silence is violence because it leaves the other person to imagine all manner of negative things about themselves. I have only used this method with people I decided I really didn’t like after I got to know them.
Ultimately, your break-up method says more about you and the way that you want to honour or dishonour what you shared with the other person.