Telefonumun şarjı bitti.

15:48 Jan 10, 2013 

I am sure that what you say would be fine in UK English too, but apart from the word for this type of phone being different, the present perfect would have to be used: "My mobile (phone)'s died."

15:28 Jan 10, 2013 

@ SeiTT. You can say it in many ways and yes, I think the British and American English differ greatly. My wife always says what I proposed. Also "my phone needs charging" may indicate low battery level, rather than the phone being in a non-operational state i.e. completely shut down. When the battery level is low, using "... needs charging" would suggest that your battery would be completely dead if not charged soon. Just an idea. You're a native speaker. I should stop here :)

11:44 Jan 10, 2013 

I haven't ever been to America but according to (almost) all Hollywood movies and American TV shows, people generally says "my battery is dead". This is why some answers include "death" :)

08:47 Jan 10, 2013 

Many thanks to you all.

Inspired by your answers, I did some Googling, and I think that "My phone needs charging" is probably best in UK English; however I have no doubt that US English may well differ greatly here.