The LittleBigPlanet series has an expansive DLC wardrobe, including level packs and themed costumes, but it seems like none of it will ever go out of style - all free and purchased content released for LittleBigPlanet and LittleBigPlanet 2 will carry over to the PS3 and PS4's LittleBigPlanet 3, a PlayStation Blog post
Past content can be transferred via a "simple re-download from LBP3's in-game store," which packs it all back into the PopIt menu that hovers beside your character. Progress made in yesteryear isn't forgotten, either - "every single Costume Piece, Material, Object, Music Track and any other creative goodies that you have collected in your previous adventures" can also be brought into LBP3.
As a refresher, any meticulously-crafted levels you made in previous LBP games can be found in the continuation of LittleBigPlanet Earth, which will let you "pick up exactly where you left off with your published creations." Custom-created content can also be transferred to a PS4 by publishing levels littered with related Prize Bubbles, then returning in LBP3 to pick up those materials.
LittleBigPlanet 3 will be available on PlayStation 4 and PlayStation 3 come November 26th.