I personally love her first album because of Password 486. Her first Japanese album, Go Younha, is good and so is the Korean remake, Comet. Houkiboshi is such a great song and the main reason why I fell in love with her.
The second part of her third album, Growing Season, is really good as well. Say Something, 편한가봐(must be easy), 헤어진 후에야 알 수 있는 것 (Something that can be understood after a breakup), and I like You are my favorites in that album. There is another song, LaLaLa, it is not the greatest song, but tune and everything are so sweet that I love it.
Her new album is really good as well, the one I posted is just an awesome song.
As for Clazziquai, for some reason I have not heard of them.