Tengen Toppa Gurren Lagann is an awesome one. The plot will wierd you out for the first 8 episodes, but once you get through it, the scale of epic will go off the charts. Watch it!
Plot quoted from Anime News Network:
In their closed-off underground village, Kamina and Simon chafe at the limits imposed by the village elder. Yet all this will change, when Simon stumbles across a fantastic device - just as the village's peace is broken by a violent intrusion.
Clannad is a definate and watch Clannad After Story afterwards for sure, since I loved Clannad After Story better. (One of the few series I can say that I liked the 2nd season better than the 1st)
Tomoya Okazaki is a third year high school student resentful of his life. His mother passed away from a car accident when he was younger, causing his father to resort to alcohol and gambling. This results in fights between the two until Tomoya's shoulder is injured in a fight. Since then, Tomoya has had distant relationships with his father, causing him to become a delinquent over time. While on a walk to school, he meets a strange girl named Nagisa Furukawa who is a year older, but is repeating due to illness. Due to this, she is often alone as most of her friends have moved on. The two begin hanging out and slowly, as time goes by, Tomoya finds his life shifting in a new direction.
If you like Clannad and haven't watched Kanon, you should watch it as well. Created by the same company. :D
Yuichi Aizawa returns to this city after seven years. In his childhood, he often visited it, but something happend in the past which caused him to block out his memories of the events of seven years ago. On the day after he gets settled in, he meets a girl carrying a backpack with wings on it. Her name is Tsukimiya Ayu and he begins to recall the memories he had lost.
Darker Than Black is another good one if you like action. One of my favorites.
In Tokyo, an impenetrable field known as "Hell's Gate" appeared ten years ago. At the same time, psychics who wield paranormal powers at the cost of their conscience also emerged. Hei is one of the most powerful of these psychic agents, and along with his blind associate, Yin, works for one of the many rival agencies vying to unlock the mysteries of Hell's Gate.