Step 1: Change your profile picture
One privacy precaution Facebook added is an updated cropping tool. Up until recently, the site's cropping tool didn't actually crop your profile picture, it just cropped your picture for the small version and displayed the full photo when you clicked on the thumbnail. Now, the cropping tool crops both your small photo and your full-size photo into a square (of two different sizes, of course).

Just be aware that if you're using a profile photo cropped with Facebook's old tool, people will still be able to see the full, uncropped image when they click on it. That could be a problem if you were strategically cropping something out. If that's the case for you, consider deleting the photo and uploading it again.
Step 2: Use a small photo
If you don't want your high-res photo splashed all over the Internet, crop and resize it prior to uploading it. Using an imaging tool such as Adobe Photoshop or Microsoft Paint, crop your photo into a square and then resize it to 180 by 180 pixels.

When you upload it to Facebook, it will be just a hair larger than the small version of your profile picture, and when people click on it, they won't get a blown-up version.

Step 3: Change the individual privacy settings of your current and past profile pics

By default, all of your profile pictures are public. In other words, not only can strangers view the full-size version of your current picture, they also can flip and previous profile photos that you haven't deleted in their full-size glory.

To change this, open each profile picture and go to Edit, click the privacy button, and under Who should see this?, choose More Options and then click Only Me. You must do this separately for each photo in the album, including your current profile picture.

If you leave your current profile picture set to Public, then strangers will be able to see likes, comments, captions, and other photo data, such as location and tags.