The Gemara in Masechet Yebamot (62b) teaches that grandchildren are considered like children. One application of this principle is the ruling of the Rama (Rav Moshe Isserles, Poland, 1530-1572) that the obligation of Kibbud Ab Ve'aem (honoring parents) includes a requirement to give honor to one's grandparents.
Accordingly, Hacham Ovadia Yosef ruled that there is a Misva to recite Kaddish for a deceased grandparent, as this benefits the grandparent's soul and thus fulfills the Misva of Kibbud Ab Va'em. Indeed, the Kensset Ha'gedola (Rav Haim Benvenisti, Turkey, 1603-1673) writes that he instructed his sons to recite Kaddish for their grandmother. However, if one's parent is still alive, he should first request the parent's permission, as some people do not feel comfortable with their children reciting Kaddish.
Although it is a Misva to recite Kaddish for a grandparent, this is not commonly done, unless there is nobody else to recite Kaddish for the grandparent.
Hacham Ovadia cites Rav Menahem Azarya Mi'Fano (Italy, 1548-1620) as stating that there is no obligation to recite Kaddish for one's deceased wife. Nevertheless, it is customary to do so, and a husband's recitation of Kaddish for his wife brings greater benefit to her soul than Kaddish recited by somebody who is not related to her.
Summary: It is a Misva to recite Kaddish for a deceased grandparent, provided that one's living parents allow him to do so, though this is not customarily done unless there is nobody else to recite Kaddish for the grandparent. It is customary to recite Kaddish for one's deceased wife, even though this is not strictly required.