for anime:
Madoka - I'm a huge fan of tragedies, and Madoka pulls it off so well!
Cowboy Bebop - Probably my favorite set of characters I've seen in an anime.
Tamako Market - I really enjoy the slice of Life genre and Tamako's is at the top of my list. (Can't Wait for the film^^)
Spice and Wolf - Currently reading the Manga and found interest in the anime and It was truly beautiful.
Baccano! - probably my favorite story out of most animes I've watched.
For Manga:
Attack on Titan - The anime was amazing but I couldn't hold myself back when it ended so I had to read the manga which I caught up to in a matter of hours.
Spice and wolf - Started reading around its release, it claims to still be ongoing but I've waited years for a new chapter to be released.
Negima! magister negi magi - I was looking for a magical genre and found this little gem. though it's filled with a lot of fan service it had it's moments that stood out and is probably the biggest set of manga volumes I own.
Black Butler - Something about Victorian London always has my interest for some reason.
A town where you live - Not exactly sure why this is here because It's been at more than 3 years since I last read it and haven't bothered to catch up since, but I do recall getting emotional over some parts in it, then again I was only 15 at the time so I could just be overreacting.
Honorable mentions - UQ holder (sequel to negima), To Love-ru, (what got me into reading manga when the series was first released, haven't caught up with the series), My Balls (A wierd manga I read when I was younger and thought it deserves some attention xD)
BONUS
these didn't make it to the favorite anime list because I haven't finished watching them. but I did play the Visual Novels and thus would recommend you watch the anime adaption of the following:
Steins;Gate, Clannad and Clannad after story, AIR, Little Busters, Ef: a Tale of Memories, and Kanon(2006 version).
Don't hold me to this list because for all I know the show would try and pull what school days did and pair the main protagonist with every female character in the show. but most of these from what I hear are pretty good!