Right on the horizon is another example -- Olympus Has Fallen directed by Antoine Fuqua and starring Gerard Butler will tell virtually the same story about terrorists invading the White House and holding the President hostage as White House Down directed by Roland Emmerich and starring Channing Tatum.
Here are some others that come to mind, in no particular order.
Mirror Mirror vs. Snow White and the Huntsman - The fairy tale adventure came to life in two competing films with big names in the role of the wicked queen. The first was directed by Tarsem Singh and starred Julia Roberts and the second, which was a bigger hit, starred Charlize Theron.
Deepstar Six vs. Leviathan vs. The Abyss vs. Lords of the Deep - Not two, not three, but four action/horror movies came out set in underwater settings over 12 months in 1989. That's not counting a bunch of low-budget ripoffs. The most memorable of the bunch was James Cameron's underrated Abyss, which revolutioned digital special effects.
Dante's Peak vs. Volcano - Disaster movies were in vogue, but these two movies, one starring Pierce Brosnan with Linda Hamilton and the other starring Tommy Lee Jones with Anne Heche were very similar, although Dante's Peak has been lauded for being more historically accurate.
Deep Impact vs. Armageddon - Who could resist two end of the world by wayward meteor/asteroid movies? Not me. I saw them both.
Antz vs. A Bug's Life - Although the Pixar flick might have more longevity, Antz is still my favorite of the two, with the voice talents of Woody Allen and Sylvester Stallone, among others.
Mission to Mars vs. Red Planet - John Carter may have hurt the box-office drawing power of the fourth planet from the sun, but there was a time when major director Brian DePalma and star actor Val Kilmer dueled it out with stories set on our celestial neighbor named after the god of war.
The Truman Show vs. EDtv - How can such similar plots spark two movies with release dates so near each other? A man's entire life is captured on television in both these flicks, one starring Jim Carrey and directed by Peter Weir, the other starring Matthew McConaughey and helmed by Ron Howard.
Tombstone vs. Wyatt Earp - Although Kevin Costner's all-star version of the gunfight at the O.K. Corral had the biggest expectations, it was Tombstone with Kurt Russell and Val Kilmer that became a sleeper hit and cult classic.
Like Father Like Son vs. Vice Versa vs. 18 Again vs. Big - You know Hollywood is begging for ideas when it releases four (count 'em) movies about kids who bodyswitch with adults. The Tom Hanks comedy Big, directed by Penny Marshall, became the blockbuster success story of the group.
K-9 vs. Turner and Hooch - Cops and dogs. 'Nuff said.
Christopher Columbus: The Discovery vs. 1492: Conquest of Paradise - The year was 1992, the 500th anniversary of the voyage of the Nina, the Pinta, and the Santa Maria, so it's somewhat understandable that there were two major motion pictures about the man credited with bringing Europeans to the New World.
Chasing Liberty vs. First Daughter - Mandy Moore played the rebellious daughter of the President of the United States, and in a similar romantic comedy at just about the same time, so did Katie Holmes.
The Illusionist vs. The Prestige - The year 2006 saw two period dramas about magicians, one with Edward Norton, and the better one with Hugh Jackman and Christion Bale, directed by Christopher Nolan.
Despicable Me vs. Megamind - Here are two computer-generated cartoons focusing on supervillains, both released in 2010.
Iron Eagle vs. Top Gun - Jet fighters were the real stars of these two movies.
Kundun vs. Seven Years in Tibet - Who knew the Dalai Lama would inspire two motion pictures about his life during the same year, one directed by Martin Scorsese and the other starring Brad Pitt?
Capote vs. Infamous - Truman Capote's life was the subject matter of two critically acclaim competing films.
Lambada vs. The Forbidden Dance - Hey, it was 1990. Forgive them.
Dr. Strangelove vs. Fail-Safe - One was a satire by Stanley Kubrick (and one of my favorite movies of all time) and the other was a drama by Sidney Lumet, both dealt with a fictional Cold War nuclear crisis.
There are surely a bunch of others. Let me know if you come up with any others you want to share.