You can't like a Page on behalf of a user (Bugzilla discussion). You can, however, like posts, comments, and photos on behalf of a user.
Edit 7/9/2012
Since bugzilla no long exists, the bug linked above is inaccessible. Google doesn't have a cached version of the page, so I ran another search. The best thing I could come up with was this Google Code Discussion regarding the ActionScript API.
Facebook makes brief mention of Publishing likes via the Graph API in the documentation, but doesn't say one way or another whether you can like a Page on behalf of a user - just "Objects" which (probably arguably) are not "objects" in Facebook-lingo.
My thought is, the API to like page is available, but is only offered to white listed applications (such as, the Facebook iOS and Android applications) written by "special" publishers. There's obvious reasons why Facebook wouldn't want/allow developers to create like connections on the graph. It would be taken advantage of by spammers and other nefarious developers and would deteriorate the meaning of what a "like" represents for a page on Facebook.
My guess is, you'd have to make a pretty strong case to Facebook about why you need/want access to the Page's Like connection (for publishing) before they'd even consider giving you access. I'd also guess that they'd want to verify that you're doing only user initiated like creations (in such a way that the iOS application would handle it) so as to protect the reptutation/meaning of a "like" action.