Is it safe to turn the iPhone 4 off for over a week I am going away on holiday for a week but don't want to take my phone with me because I'm afraid of running up a huge bill, is it safe to turn the phone off for this long? Or can it damage the battery?
This answer is somewhat outdated as Apple has added very robust and intelligent overcharging, over rate charging, temperature controls and adaptive charging to extend the life and avoid many of the situations where 2010 to 2015 era battery and charge system tech could result in less service length than ideal.

Even for 2010 era, what is described is still certainly safe - just turn it off and enjoy your trip. Newer gear makes this even more safe to do. You really have to go out of your way to exhaust batteries - and only random failures result in swaps in my experience now.

iPhone and all other Apple Products shipping in the last 5+ years (excepting the Apple Battery Charger which are NiMH AA cells) have lithium polymer (lipo) batteries. The MacBook Pro and Air batteries are a bit more sophisticated than the iPhone/iPod/iPad batteries but the underlying chemistry is the same.

It is safe to store them for months and it's best to charge them 50% and turn off the device for long term storage. All lipo batteries work best when they get a normal serive charge and discharge cycle once a month, but slowly draining from 50% to 0% over 6 to 12 months and then getting charged back to 50% is quite safe for several years of storage.

I wouldn't worry about leaving it off even 5 months if you starting over 50% but less than 70% charge in a not-hot location.


The worst thing for a battery is to
use or charge it above 95 degrees F.
The next worst is deep, deep
discharge (well past when the device
shuts off) - make sure you charge up
the battery past half before long periods of 
storage.
Repeated long storage while full.
(don't make a habit of leaving it
100% full and off for months at a time)


I still have my original iPhone going strong (for occasional testing) by waking it up every 6 months at a minimum. If I leave it around 2/3 full and wake it six months later - it's usually got more than 1/4 battery left. I then use it for a few days charging and discharging fully before shutting it off again.