While May belonged to Marvel - thanks to Iron Man 3's billion dollar box office - there is no question that June belongs to DC. In the past, it has been Batman that represents the DC Comics brand, but this year that task befalls a more colorful superhero. Man of Steel is arguably June's most anticipated release, and its success could help pave the way for an entirely different cinematic universe. No pressure.
Superman aside, June is surprisingly heavy with comedies, but there's a nice variety even within that genre. There's the annual Pixar release for the families, two R-rated comedies for the adults, and an "inbetweener" comedy featuring Vince Vaughn and Owen Wilson. In other words, it's a great time to go to the movies.