One of the beauties of using a phone running Google's Android operating system is that you have easy access to online backup tools from Google. This "cloud" backup means you don't have to worry about backing up to a computer, though doing so can bring added protection. Note that you'll need to enable both "back up" and "sync" settings on your phone to maximize the amount of data that is protected against loss.
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Set up a Google account on your phone, or add an existing account, if you haven't already done so. Your phone will need to know your Google account to be able to back up data to Google's servers.
Tap "Settings," then "Privacy" and then check the "Automatic restore" and "Back up my data" options, if they aren't already checked. This will enable you to restore data, if the relevant files on your phone are deleted or damaged.
Tap "Settings" then "Accounts and sync," then check the boxes for each of the listed types of data that you want to sync. You may have to tap the Google icon with your account name to access the check boxes to access specific Google services for syncing. These settings go a step beyond a simple backup; in addition to making sure any changes to your data are reflected in the copy on Google's servers, it will also keep your phone up to date if you change the relevant data via another device, such as your computer.