I would like to display the users profile picture inside of my applications canvas page, is there a way to do that using the graph api?
I know I can do it using FBML
EDIT: So facebook has changed it again! No more searching by username - have amended the answer below...
https://graph.facebook.com/{{UID}}/picture?redirect=false&height=200&width=200
e.g. https://graph.facebook.com/4/picture?redirect=false&height=200&width=200
Facebook Graph picture doc
One very important thing is that like other Graph API request, you won't get the JSON data in response, rather the call returns a HTTP REDIRECT to the URL of the profile pic. So, if you want to fetch the URL, you either need to read the response HTTP header or you can use FQLs.
You can also resize the profile picture by providing parameters as shown below.
https://graph.facebook.com/[UID]/picture?width=140&height=140
would work too.