This tutorial will show you how to easily view anybodies profile picture in full size without being their friend. I found this out when playing around with how Facebook stores images I found that what they do is quite predictable and found this out.
Why would you want to see a full size picture of someone?
Maybe they sent you a friend request, you can't see their face from the profile thumbnail and there privacy settings don't allow you to see their full size profile picture.
There are three methods I will show you set by step, the first two show you how to view full profile pictures which I recommend but the third only allows you to see a small 100x100 photo but I thought it was cool as it used the new Facebook graph search function so I included it.
Method 1: Will view full profile picture (Easiest)
Step 1, Right click on the profile picture thumb nailStep 2, Click on "Copy Image URL"
Step 3, paste it into your URL bar it should look like this;
Remove the

Step 4, click enter and you should see a full size image of their profile should appear.
Method 2: Will also show you the persons full profile, similar to Method 1
Step 1, Again right click on the profile picture thumb nailStep 2, Again click on "Copy Image URL"
Step 3, paste it into your URL bar it should look like this

Step 4, Copy the last part,

Step 5, Put this into your URL
"https://fbcdn-sphotos-f-a.akamaihd.net/hphotos-ak-ash4/"
(Left in so you can copy and paste)
Then paste after

Step 6, press enter and you should see a full size profile picture
These two methods will show you a full size profile picture of the person, they are very similar and rely on Facebook being predictable in the way they name photos on there image hosting servers.
Method 3: Not as good shows a 100X100 profile picture
Step 1, Go to the persons profileStep 2, Find out the persons Facebook username;
It should be in the url for example;
Step 3, Go to;
You will see a 50X50 size profile picture and you should have been reditected to a different URL that should look like this;
Step 4, Change the q at the end of the numbers to a n, you should then see a picture that is now 100X100.
It is not the best way to see them and the image is not full size but it was one method I found out.