IFTTT for iPhone allows you to setup your iPhone's Contacts app as a channel. Once set up, you can then have the app perform various functions, all of which are triggered when you add a new contact to your device. One such function is to append your new contact's information to a plain text file on Dropbox, or as another row in a Google Drive spreadsheet. Currently there's no way to back up all existing contacts on your iPhone using the IFTTT app; only new entries.
Not only does using a recipe like this create a constant backup of new contacts, but it also helps you remember when (and potentially where) you first met someone. You can enable the recipe for a short amount of time -- say for a trade show -- and then disable after a period of time. This is perfect for those of us who frequent trade shows and have trouble keeping track of who was where.
To get started, make sure you download and install IFTTT for iPhone and enable the Contacts channel. After doing so, you can add the Dropbox-based recipe or the Google Drive-based recipe to your account.
Note that during the process you can customize the fields added to the respective files, along with the file name.
You'll need to have background sync enabled if you want the new additions to be added automatically. If not, you'll have to manually launch the IFTTT app and let it run through the recipe.