There are a handful of URL's you can use to perform some common Facebook actions by simply calling them using a well formated URL. Here are handful of commonly used actions available via links (subsititue XXXXX with the user's Facebook ID or YYYYY for other data). These can be used from within your Facebook application to add more utility:

GENERAL
View a Facebook user's profile:
http://www.facebook.com/profile.php?id=XXXXX

Poke a Facebook user:
http://www.facebook.com/poke.php?id=XXXXX

Send a message to a Facebook user:
http://www.facebook.com/message.php?id=XXXXX&subject=YYYYY&msg=YYYYY
- subject and msg are optional

FRIENDS
View a Facebook user's friends:
http://www.facebook.com/friends/?id=XXXXX

Add a Facebook user as a friend:
http://www.facebook.com/addfriend.php?id=XXXXX

Display what friends a user has in common with another user:
http://www.facebook.com/friends/?mutual=&id=XXXXX
- XXXXX is the id of the other user

PHOTOS/POSTS
Access photos a Facebook user's photos:
http://www.facebook.com/photos.php?id=XXXXX

Search for photos of a Facebook user:
http://www.facebook.com/photo_search.php?id=XXXXX

Read or post on a Facebook user's Wall:
http://www.facebook.com/wall.php?id=XXXXX

Read the specified Facebook user's notes:
http://www.facebook.com/notes.php?id=XXXXX

SEARCH
Search Facebook for keyword:
http://www.facebook.com/s.php?q=YYYYY

Search Facebook for People:
http://www.facebook.com/s.php?q=YYYYY&k=100000020

Search Facebook for Pages:
http://www.facebook.com/s.php?q=YYYYY&k=100000000020

Search Facebook for Groups:
http://www.facebook.com/s.php?q=YYYYY&k=200000010

Search Facebook for Applicationd:
http://www.facebook.com/s.php?q=YYYYY&k=40000000020