Just like emails can be a mean of permanently keeping conversations, so can SMS and MMS.
if you would like to keep a backup of your SMS and MMS and would like to restore them in case you a new Smartphone, delete some by accident (or try different ROMs), here is my top 3 tried and tested solutions, which will backup your SMS and MMS to your cloud storage (as a simple backup to your SD card is next to no use if your phone gets broken or stolen).
SMS Backup + https://play.google.com/store/apps/details?id=com.zegoggles.smssync
The Pros:
• Fast at restoring
• Allows to choose between restoring the last 100, 500 messages or all of them.
• Backs up your messages as email conversations in one of your Google Mail folders. Thus even if you don't have access to your smartphone, it allows you to still read online the SMS you have sent and received, as email conversations.• Gives you a progress while the messages are being restored.
The Cons:
• No local backup on the SD card, so without an Internet connection you won't be able to restore your messages.
SMS Backup & Restore https://play.google.com/store/apps/details?id=com.riteshsahu.SMSBackupRestore
The Pros:
• Local backup on the SD card as well as giving plugins to backup to your cloud storage (backup to the cloud needs the Pro license), so even without an Internet connection you can restore your messages.
• Messages are backed up into an XML file which is an open standard
• Allows you to choose the specific messages you want to restore, or from a specific date or all of them. However be advised that it appear to take just as long if not more to restore messages, say from the last 10 days as all of them, because the application scans all of the messages to check if they are within your specified the date range.
• App more carefully designed and thought through than SMS Backup +
• Gives you a progress while the messages are being restored.
The Cons:
• Slower to restore than SMS Backup +
• I’ve had instances where it seems to duplicate messages in the database after several restore, increase the number of messages and the size of the XML database.
Titanium backup https://play.google.com/store/apps/details?id=com.keramidas.TitaniumBackup
The Pros:
• Local backup on the SD card as well as backing to your cloud storage (backup to the cloud needs the Pro license), so even without an Internet connection you can restore your messages.
• Fast at restoring.
The Cons:
• No option to choose if you want to restore messages from a specific date nor a specific amount of message. It’s either all or nothing.
• No progress whatsoever of the messages being restored so you can't estimate when the restore process will be finished.
• You phone needs to be rooted to use Titanium Backup.
Personally I use SMS Backup + and install it on other people’s phones that I configure but as I also use Titanium backup as I have it on my own phone.