Can your cell phone have service when you are out of the US?

Yes you can. You need to check with your service provider to ensure that you have international roaming activated on your service. You need to note that using your handset in any other country apart from your home country can be extremely expensive. If your travelling and want to use your handset abroad, ask your network provider to put a daily spending limit on your service, in order that you don't over spend. Using data is very expensive, that should be avoided. If local wifi is available use that instead, most hotels usually provide free wifi to their guests. If you are on a PAYG handset, it is best to buy minutes, texts and data in advance. See what extra packages are available from your provider as these are normally good value for money compared to not using them.