There are many spoilers on the above page so only click if you don't mind.

What is Jaqen H'ghar Doing?

When Jaqen leaves Arya (with the Braavosi coin and the phrase "valar morghulis," which eventually brings her to Braavos and the Faceless Men), that's not the last we see of him. It is undoubtedly Jaqen in the prologue to A Feast for Crows, who – in the guise of the Alchemist, the face Arya saw him change into right before he left her – murders the novice Pate at the Citadel… the same Citadel where Sam Tarly has gone to become a Maester and research the Others… and who meets the same Pate, alive and well. So Jaqen is definitely at the Citadel, disguised as this Pate. Seeing as the Citadel is the most learned place in the world, it seem Jaqen is trying to learn something… or to prevent someone else from learning something. The real question is if he's working for someone specific, or on behalf of all the Faceless Men? (For more, continue reading here.)

Another fun question: What does Varys want?

And of course: Is Syrio Forel alive?

Also see here:

http://pandawhale.com/post/16944/is-syrio-forel-alive-and-other-game-of-thrones-theories

There's a lot more questions about Jon Snow and Tyrion Lannister at the link.