No doubt there will be numerous threads on this subject, so I thought I would pre-empt them and create a sticky.
Can I buy a phone in the US and use it over here?
Yes, but it must be the GSM/AT&T model, purchased SIM-free directly from Apple. Handsets purchased from Verizon will not work with the GSM carriers here as they do not take a SIM card. Handsets purchased from AT&T usually come with a minimum-term contract and are locked to the AT&T network.
Can I use my Vodafone/Meteor/Three/Other SIM in an iPhone purchased from a mobile carrier?
No. Not until you Jailbreak it and Unlock it, or have your carrier Unlock it.
It is important to note that some Irish carriers are now unlocking iPhones officially - please consult your carrier for more info.
I purchased my iPhone directly from Apple. Is it unlocked?
Yes. iPhones purchased from Apple.ie or from Apple stores are factory unlocked.
Jailbreak? Unlock? Sounds scary.
They are not really. iClarified have a jailbreak wizard to show you step-by-step how to jailbreak any device here.
What's the difference between Jailbreaking an iPhone and unlocking it?
Jailbreaking allows you to install non-App Store programs. Unlocking it allows you to use the iPhone on any GSM network.
Can't I just buy an unlocked phone?
You can, but only directly from Apple or authorised Apple retailers (or on adverts.ie / eBay). It is simply a matter of walking into a phone shop and purchasing one, bringing it home, and popping in your SIM card. You cannot purchased unlocked iPhones in the USA, as they are locked to AT&T.
How do I jailbreak / unlock my iPhone?
If your carrier will not unlock your phone officially, then you will need to jailbreak & unlock.
See the unlocking wizard on iClarified here.
At the time of this writing, all iOS devices & every iOS can be jailbroken. However, newer devices and iOS's require a "tethered" jailbreak.
Tethered - If your device is ever powered off, you will need to connect it to a computer and run redsn0w to turn it back on.
iOS 3.1.2 - 4.0.1
Every device on iOS versions 3.1.2 - 4.0.1 can be jailbroken by visiting http://www.jailbreakme.com in safari on their iDevice.
iOS 4.0.2 - 4.1
Every device on iOS versions 4.0.2 - 4.1 can be jailbroken with redsn0w.
iOS 4.2 (4.2.1)
Some tethered, some untethered.
Every device on iOS 4.2 (4.2.1) can be jailbroken with redsn0w.
However, the following devices require a tethered jailbreak on this iOS:
iPhone 3GS New Bootrom
iPod touch 2nd Gen New Bootrom
iPod touch 3rd & 4th Gen
All others have an untethered jailbreak.
redsn0w - Windows
redsn0w - OSX
Currently, the following basebands can be unlocked:
01.59.00 (iPhone 4)
04.26.08 (iPhone 3G/3GS)
05.11.07 (iPhone 3G/3GS)
05.12.01 (iPhone 3G/3GS)
05.13.04 (iPhone 3G/3GS)
06.15.00 (iPhone 3G/3GS)
If you are on a qualifying baseband, simply run cydia on your jailbroken iPhone and install "ultrasn0w".