MySQL Database Backup

I’m a newbie,
is there any way to store all my blogs on a file, because I’m using WordPress on my website, and i pay for the hosting monthly. now i’m not satifised with my current hosting service, and I decided to move to another. now the problem is that all my blogs are saved in MySQL at the hosting company.. i wonder if there’s any way to move everything to a new hosting company’s server..
i hope my questoin is clear enough..
Thank you very much!!!!