Yup, there are any number of SMS backup apps you can use, but I have that one running a weekly scheduled backup for me. You don't have to use a message app with the feature, it can be entirely independent of which message app you prefer.
That said, some of the "phone transfer" apps that most phones come with will also do this for you. But a backup stored off-device (in the cloud if you like) means you don't lose them if something happens to the phone either.