Death Note is probably my all time favourite. It's dark but not too dark, so it has a kind of mysterious atmosphere to it. Also, the characters are all ace, they all have interesting personalities and traits as well as what happens to them. The story is brilliant, they created such a cool idea and world and showed how emotion can sometimes get the better of you. Then the whole storyline with L was absolutely brilliant, the deducting skills were so good they were almost hard to catch up with. Some people disagree with what happened but I thought everything was done really well. The Shinigami world was such a cool idea, it really intrigued people as well. The rules of the Death Note are great because people can learn them and it's something you can learn about and explore possibilities with because it's a whole different world and idea. It's unique and it really shows a very realistic situation where the good guys don't always win. Obviously in Death Note they do but through a much more real story and struggle. I love how you end up on the edge of your seat with anticipation, each person learns to love a different character and wants them to win, which is really fun to watch. Plus both the English Sub and Dub are excellent. The other great thing about it, it's not very predictable, it's quite hard to see certain events coming. So overall, that's my favourite.
Angel Beats and Clannad are close second. Angel Beats is a short anime, but that doesn't make is any less brilliant. The world isn't as original, but the story line really is. It's a great idea and it has a lot of emotion behind it. The characters are all really likeable and you can often empathise with them too. It's also action packed, lots of cool fights and the descent to the underground base (Guild) is so funny to watch as they can't die in that world but so many of them 'die' via traps. It really is a shame Angel Beats isn't very widely known, that's probably because it's a relatively new anime that doesn't have a manga yet either. The characters are great, though and each one has an interesting, individual story as to how they died and why they are in this world rebelling against the God letting them disappear. (You have to watch it to understand.) But the anime has everything, action, humour, drama, romance. Which is what makes it great.
Clannad is also one of my favourites, probably because I quite like sad, soppy things from time to time. The Afterstory is almost painful to watch because of the sadness but luckily the end made me breath a sigh of relief and the ending is absolutely brilliant. The storyline is cute and fun to follow but the ending links in with everything and makes you go "Ohhhhhh...." I loved the characters from that anime, it was really funny too. It really makes you reflect on life more and think about the people around you. What I also loved about Clannad is that it followed one main storyline in the background if you like, but then a lot more smaller stories throughout the anime. It introduces you deeply to each character so that you really want to sympathise and get to know the character. There's a lot of humour in that anime too, as well as romance and just life really. There are some pretty big things that happen in Clannad, but if you can handle the weepy moments it is great.
Hetalia is excellent for short bursts of comedy. Each episode is only 5 minutes long and despite what you might think it is still great. It takes every historical event, and every country's stereotypes and turns them into anime characters getting into various trouble with each other that reflects real history. It's just laugh out loud funny and the stereotypes really made me giggle, the characters are really well done. I actually prefer the English Dub of this series, purely because in the dub you can hear the accents of each country, which just makes it even more funny.