One very interesting thing I discovered through my studies is that Japanese has a lot of words that are very similar to other words, but have a slight variation in meaning. For example, back when I was at Fujitsu, I learned the difference between 完了 and 終了, which both mean "to finish" but have slightly different connotations (the former implies that a task was completed, while the latter implies that something ended [but not necessarily completed], e.g., プロジェクトを完了しました [I completed the project] and プログラムが終了しました。[The program ended]).
Here are some additional groups that I noticed:
考える (to think, consider) vs. 思う (to think) vs. 検討する (to consider)
仕事 (work, job) vs. 作業 (work)
完了 vs. 完成 (both meaning "to finish, complete")
去年 vs. 昨年 (both meaning "last year")
変える vs. 変わる vs. 変化する (all meaning "to change")
大統領 vs. 社長 (both meaning "president")
開く 「あく」 vs. 開く 「ひらく」 (both meaning "to open"; notice that they are written exactly the same but pronounced differently)
行く 「いく」 vs. 行く 「ゆく」 (both meaning "to go"; same situation as above)
見せる vs. 示す (both meaning "to show")
閉める vs. 閉まる vs. 閉じる (all meaning "to close, to shut")
必要する vs. 要る (both meaning "to need")
It would be very interesting to see the differences between these words.