Dr. Strange believes Wong lacks a sense of humor and never laughs.
However, at the end of the movie, after Dr. Strange made his bargain and cast out Kaecilius and his minions, Wong laughed like a drain.
What's so funny in this?
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You have to pay attention to the dialog throughout the movie. When Steven Strange first discovers the Eye of Agamotto, he reads an ancient manuscript which instructs him on how to manipulate time. Wong and Mordo rush in and stop him, and Wong angrily tells Strange that his actions could have had serious consequences (creating a time loop, or altering the future in an unwanted way). He asks Strange why he didn't heed the warnings in the book. Strange says:
They really should put the warnings at the beginning of spells
Now, skip to the end of the movie, where Kaecilius and his minions have just been dragged into eternal torment by Dormammu. Dr. Strange says:
You really should’ve stolen the whole book because the warnings come after the spells.
Wong obviously finds the irony in this funny, thus why he laughs for the first time in the movie.
Another possibility that has been raised on sites like TVTropes is that it's about master-subordinate systems, and a callback to an earlier exchange where Strange points out that people usually laugh at his jokes, and Wong queries whether those people are subordinates. Strange's prior jokes are uttered with the expectation of laughs. This one is spontaneous, and after he and Wong are on an even footing as friends and comrades.