The main plot involves a company called Setec Astronomy, which makes a box capable of decrypting all the encryption codes used in the United States. As the main characters discover, Setec Astronomy is an anagram of "too many secrets."
In the opening credits, the names of the production companies and principal cast and crew first appear as anagrams before rearranging themselves into the correct spellings.
Bruce Sterling has pointed out that the title itself is an anagram for NSA REEKS.
In The Monster Squad, the lead character correctly deduces that the "Mr. A. Lucard," who wants to talk to him about the diary of Van Helsing, is, of course, Dracula.
One of the initial plans for The Long Kiss Goodnight. Samantha Caine wasn't originally Charly Baltimore's alias. It was originally going to be because "Sam Caine" is an anagram for "amnesiac".
Meta example: October Sky got its title because it's an anagram of Rocket Boys, which was the title of the book on which it was based.
Anamorph has Aubrey trying to find a Gerri Harding (Red Herring) and trying to decode a repeated phrase from the killer, "A poison harms" (Anamorphosis).
The Babadook is about a single mother and her son who are being tormented by a malevolent monster called Mr. Babadook. The monster was summoned when they read a creepy-as-hell children's pop-up book. The name is explained as the noise you hear when he enters your lives: a rumble followed by three sharp knocks. Ba...ba...DOOK! DOOK! DOOK! But it doubles as an anagram. Babadook: A Bad Book.
A Meta example: the Ewoks in Return of the Jedi were originally planned to be Wookies. Rearrange the word Ewok and you almost get what they were before Lucas decided to give the cash cow a bit more squeezing.