I am traveling to Europe later this month and I have an iPhone 5. What companies offer prepaid SIM cards that work in Spain, France, and Italy, if there are any?
the iPhone 5 is CDMA and GSM compatible.
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You'll be hard pressed to find a sim card that won't work in all three countries if it works in one.
But, as has already been pointed out, the cost of calling and receiving calls will be significant. At least until roaming charges will be limited from late next year onward (if my memory serves me well).
In the mean time, you could consider a 'universal' sim card, like this one:
I think all the major carriers will work but can cost you a huge pile of money.
T-mobile has a free (no additional cost) data/text plan with their Simple Choice plan. http://www.t-mobile.com/optional-services/roaming.html