Using v3.2.1 as of March 20, 2013 of Facebook SDK.
NSString *fbAccessToken = [[[FBSession activeSession] accessTokenData] accessToken];
If you prefer dot syntax,
NSString *fbAccessToken = [FBSession activeSession].accessTokenData.accessToken;
For those using Swift;
var fbAccessToken = FBSession.activeSession().accessTokenData.accessToken
Update for v4.1.0 SDK onwards
Objective-C
NSString *fbAccessToken = [FBSDKAccessToken currentAccessToken].tokenString;
Swift
var fbAccessToken = FBSDKAccessToken.currentAccessToken().tokenString
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