This is definitely a kendo tenugui. It reads from right to left and says "sword heart/mind, bright way" meaning, I think that to develop a sharp mind like a sword makes your path in life clear and bright. I think this is beautiful shuji (calligraphy).
This one was a souvenir from the famous Buddhist temple "Ryoanji" in Kyoto. The design depicts the reason the temple is so famous, its stone garden.
This is the club tenugui of the Ryujokan dojo in Kumamoto. It was produced as a limited edition for the 1992 Australian Kendo Championships in Melbourne. It is based on the Ryujokan joseki, the character "ken" with a long 'tail'. Here it is sideways.
This tenugui is a souvenir of Kagoshima in southern Kyushu. It has two of Kagoshima's most famous sons: Okubo Toshimichi and Takamori Saigo. Both men were very important participants in Japan's modernisation about 120 years ago. The shuji reads "Revere Heaven, Love Humanity". Saigo was the inspiration for the film "The Last Samurai" and his picture is everywhere in Kagoshima.
This is a copy of the "Heart Sutra" a very important text in Buddhism. It's a bit like having a passage from the Bible or the Koran printed on a teatowel. Most Japanese are Buddhist and also Shinto (another Japanese religion). The Heart Sutra is very common thing to find on souvenirs in Japan. It is even printed on coffee mugs!
This image of a wave is on an extra long tenugui designed to be used in traditional Japanese dance. I love how it always looks like it's about to swamp the rest of the tenugui.
Let me know if you would like to see more of my tenugui collection.