Well, what are your interests?
What anime do you like and have seen so far?
I'm going to recommend you these, they are always good ;p
Monster - Like a thriller kind of mystery manga. About a well paid and happy surgeon who one day he is ordered to forgo operating on a critically injured man in favor of a more illustrious patient. Disillusioned by the hospital's politics, he decides from then on that he will do what he thinks is right, regardless of politics.Some time later, a young boy and his twin sister are brought in. The boy has a bullet in his head and requires an operation that Dr. Tenma knows only he is capable of performing successfully. Just as Dr. Tenma is about to begin the procedure, the mayor is rushed into the hospital and the director instructs Dr. Tenma to leave the boy to operate on the critically ill mayor. Dr. Tenma decides that he will do what is right and go ahead with the boy's operation. The young boy's operation ends in success but the surgeons operating on the politician fail. As a result, Dr. Tenma is passed over for a promotion and his fiancée calls off their engagement. Soon after this incident, strange murders begin to occur, all of which benefit Dr. Tenma greatly. As a result, he becomes the prime suspect although the police have no evidence against him. It seems that the boy whose life he saved is heavily involved in it somehow and that there is much more to him than meets the eye. (Pasted this from
animenfo, I haven't read it myself, I will soon, but its supposed to be excellent).
Death Note - About a honor collage student, about 17 I think, who finds a book, the death note. Anyone whose name is written in this book, will die shortly. Quite a lot of people like death note, its really popular and definitely worth trying out.
Fullmetal Alchemist - About two brothers who try to use a alchemist ritual sort-of thing to bring back their mother from death. Unfortunately, the ritual goes wrong, and one of the brothers is left with a full metal body, and one is left with a metal arm. Its very good and very gripping.
Naruto - The manga is good, but the anime is filled with fillers (135 I think). A comedy / action about a boy, Naruto Uzumaki, who wants to become the hokage (Like the top guy) of the leaf village.
Hope I helped you. If you let me know what genre's you like, I can suggest more based on your opinions.