How to transfer data from my iPhone to a new cellphone?

I have an iPhone 4S. I'd like to get something new. However I'm not sure how to transfer all my data (contacts, songs pics etc.) over to the new future cellphone. If there's a way to do this without going into a cellphone carrier store please inform me! Also, am I able to transfer stuff from my ACTIVATED iPhone to an INACTIVATED new phone?

Try a software named Mobo Robo which supports transfer contacts between iPhone and Android devices!
http://www.wikihow.com/Sync-Contact-Data-Between-an-iPhone-5-and-an-Android-Device-with-Moborobo

There are two ways of going about backing up your current phone.
1. Plug it into your computer and connect to iTunes. From there you can sync everything to computer including photos, music, contacts, apps, notes, etc.
2. Utilize the iCloud feature on your phone and back-up everything into the cloud. From there, if you decide to get a new iPhone, when activating the new phone select restore from iCloud back-up and you will make a mirror image of your old phone on the new phone.

Second, you can transfer your data from your active iPhone to an inactive iPhone. Utilize one of the two methods above in order to do so. If you decide to go the iCloud route you will need to connect the inactive phone to Wi-Fi in order to retrieve the data.

If you are going from an iPhone to an Android phone, there's an iOS app called MyContacts Backup. Download that on your iPhone and it will back up your contacts. Then download the same app on your Android phone and it will download your phonebook from your iPhone. As far as transferring everything else, if your new phone ia a Samsung phone, Samsung has a software called Smart Switch, which you can download for free off their site and use to transfer everything else off of your iPhone.

If your new phone is Android, but isn't a Samsung, there are still lots of computer programs out there that can accomplish this. MobileTrans is one of them. If you're getting a new iPhone, just open up an iCloud account and backup all of your stuff onto there, and then sign in on your new phone and download your backup. Or, alternatively, just backup everything onto your computer using iTunes, then plug your new iPhone in and select "Restore from backup" when it pops up.

Yousimply straiten out a paper clip and shove it into a hole in the bottom. A memory card will then pop out. Take the memory card out of the new device and put in old memory card. Its super simple.

What is your new phone model? If it is an iPhone or Android phone, you can use a program called Backuptrans Android iPhone Data Transfer. It lets you witch data between phones directly on computer. Hope it helps.