Anime:
hmm hard question I have a couple:
Cowboy Bebop (Needs no explanation)
ef - a tale of memories (Imo the best drama/romance Anime out there, its combination of beautiful artstyle, perfect musical scores, and a deep plot with great character development made this series a Masterpiece of story telling.
Shakugan no Shana (Awesome series it has the over the top action but then it also has a lot of slow paced episodes where it really just focuses on the characters)
True Tears (Another great drama/romance and the second out of two series of this genre that I scored a 10/10 (the first being ef - a tale of memories)
Clannad (now ef - a tale of memories and True Tears I consider Drama/Romance, Clannad is a great Comedy/Romance with some drama thrown in (the real story is a lot more dramatic than the Anime (although when the next Clannad series comes out it will be on the after story of Nagisa's route which will be very tragic and dramatic))
As you can see I prefer Anime with deep story and character driven plots, not just over the top action (which is great when backed with a compelling plot)
Also these are only the Series I've completed there are several series I'm currently watching that could take a spot in my Favorites list, but I won't know until they end.
Manga:
Ranama 1/2 (the first Manga series I ever read and finished)
Love Hina (second Manga to read and finish)
Inuyasha (Well everyone probably knows about Inuyasha (it's been out for a long ass time), it's a epic fantasy adventure about the bonds of friendship, love, and the insecurities in the hearts of everyone. Reading the Manga you cannot help but grow fond of the characters and you will find yourself vowing to punish the creator if she kills off Miroku (Sango needs him, and we want a MirokuxSango baby damn it... he needs to have a child I mean he's been asking random women for one since the first chapter he appeared in lol.) If you couldn't tell I really like the Miroku x Sango couple as does probably every fan of the Manga, they have been hiding there feelings for each other for so long and to have Miroku die now that they understand each others feelings would be ludicrous.
Rosario + Vampire (100x better than the Anime, way more action and character driven plus Tsukime kicks ass and isn't just a weak human)
To-Love-Ru (just over the top hilarity and though its extremely echii, the echiiness is actually part of its charm that makes it so funny, it doesn't use it strictly for fan service sense it grounded itself as a echii comedy romance-ish from the first chapter)
Well family those are my picks, I figured I'd give a bit of an explanation on why these are my favorites.