There are scads of apps on the App Store which will offer to backup your contacts. I tried four: a free app, a $1 app, a $2 app, and a $3 app (all prices listed are USD). One was great, two were pretty good, and one was downright atrocious.
(Note: all of the apps I reviewed are "universal" - that is, designed for both iPad or iPhone/iPod touch. All are optimized for the iPhone 5, with one exception which I have noted below.)
Easy Backup ($0)
The trouble with finding a free app to backup your contacts is finding a free app which is really free, as opposed to several which are limited ver