Guin Saga, based on a series of epic fantasy novels by Kaoru Kurimoto, starts on April 5. The series is the longest-running single-writer work in the world, with 124 volumes to date-- Vertical has released the first five, if you're interested. The story revolves around an amnesiac warrior named Guin who has to find out who he is and why he lost his memories.
Hanasakeru Seishounen (which translates roughly to “Blooming Youth”) is a shoujo romance manga by Natsumi Itsuki which tells the story of a wealthy young girl who is instructed to select a husband from four possible candidates. Unfortunately, they're all pretty good candidates who become a part of her life, so it's not an easy choice. This one's also due to start on April 5.
Finally, Phantom: Requiem for the Phantom, an anime adaptation of Nitro+'s drama visual novel, will start on an unspecified date in April. The visual novel can generally go two directions in terms of tone: a romantic drama, or a dark action drama. Judging from the website, I'm leaning towards the latter. The story revolves around a teenage boy whose memories are erased and who is forced to work for a mysterious group called Inferno, working with a young woman named Ein-- also known as the Phantom.
Bear in mind that these dates can always change, by the way. Which of these are you most interested in? I kind of want to watch them all, honestly.