Yes it's possible to backup your games but you can't play it on a unmodded xbox. You have to atleast softmod it so you can play your backed up games.
Actually it's no. An FTP connection is required to back up games, and you a modified console and a dashboard to FTP.
"BANGING HEAD REALLY HARD ON WALL!!" Im gonna say this once....PLEASE READ THE FORUM!! before jumping in with a q thats been answered 9,000,000 times, take some time to read the forum, even the guy that left a message on this thread has wrote a very good tutorial regarding modding help (quadratic dude you must be getting a headache by now) I just typed "softmodding an xbox" in google, and INSTANTLY found a tutorial. I know we all have to start somewhere, but asking questions over and over, just makes people that take out their time to answer, NOT WANT to anymore. to make your backups, Quad is quite correct, you need to ftp. To play em, you either need softmod, modchip or tsop (not getting into that) as youre a newby I would say modchip is definately your best option theres MANY modchips avaiable, think of what you are gonna use your xbox for, theres cheaper and (less cheap) modchips, but none really break the bank. If you have an xbox made after april 2004, its a 1.6 (99.9% of the time anyhow) then if you cant solder youre gonna have to use something like the spider chip for solderless installation.