Web: Facebook's privacy tools are notoriously complicated and constantly changing. Stalkscan is a third-party tool that can find and highlight any information that's publicly visible (or visible to you) for a particular profile.
Stalkscan uses Facebook's built in search, which means that you'll have access to any info available to your own profile, even if it's not public. This makes it difficult to self-audit. If you want to be thorough, you can create a second account (Facebook frowns on this practice, but it's not impossible) and use the search to surface your info. Alternatively, head to your profile and click "View As" to see what it looks like from the public. Though this method doesn't offer search.
Despite its creeptastic name, Stalkscan can show you what kind of information people can already search for. For starters, you need the full link to a person's profile. Enter the profile URL in the search box and the site will give you quick links to a bunch of searches for things like that person's pictures, videos or likes. If you're searching for yourself, you'll see private photos that are only visible to you and those you've shared with, but it's still a handy way to see what people can search for.
While it sounds scary, all of this information is drawn from public Facebook searches or your own privacy settings. In other words, if you go to Facebook right now and search for "Pictures of [X person]" you'll get the exact same results as if you click the Pictures link on Stalkscan. You'll only see photos that are visible to your privacy settings. So, if you're searching for the profile of someone you're not friends with, your results will be very limited. If you're searching for yourself, you'll see your own pictures.
This is most useful if you want to discover what your friends can see about you. I tried it out on my own profile and found pictures that I don't remember from a long time ago. I was then able to make sure those all fit my preferred privacy settings. Many posts were made before Facebook gave you the option to limit posts individually, so this is a good way to filter through those. It also gives you links to searches you might not have thought to hide, like future events or places you've been tagged in. If you've never audited your public Facebook info, this is a good place to start.