In language school, our Japanese teacher told us that in Japanese writing, the type of stroke that you use is important. When learning Kana or Kanji, we should always take special note of Tome, Harai and Hane.

By now, I am wondering, how important that really is. Are there Kanji that you can only differentiate by the type of stroke? I imagine that it might be important when writing by hand, just because it will look strange.

For those who don't know about the different types of lines, this page explains it quite well.