WordPress updates don’t break a site in most cases. Each final version has been tested before the release, and the most important errors are found and fixed during that.
What could break?
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If your setup is rather rare, IIS 6 for example, or custom URLs for some directories, then it might happen that this breaks, because the testers missed that.
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Your theme or some plugins might be very old oder not written properly. If they rely on an outdated version of jQuery and WordPress comes with a new version, not all scripts might work anymore.
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Some changes are really hard to see. When Matt added the filter
WordPress → WordPress, some authors got in real danger: Capital letters inside of words are not allowed in some countries, they are reserved for religious terms or names. The punishment includes torture and imprisonment. This was never mentioned in the release notes …
I recommend to run a local mirror of your site on your computer with all the plugins and the theme you use on the main site. Run the update locally first; if nothing breaks you should be safe. Database breaks are really, really rare.
But still: backups are cheap. Make one regularly.