Well, something simple. The Scandinavian word for "I" is "Jeg," or "Jag," which curiously sounds very similar. (The G is silent, a trait of Scandinavian and the English languages.)
In Old English, the word for "I" is "Ic." (pronounced "itch".) "Ich," the German word for I, sounds similar, and is also orthographically similar.
The word for "You" in German, in its informal form, is "du," however, is much closer to the word "thou" in certain cases. "Thou" is obsolete in today's modern English.