The removal of the ovaries together with the Fallopian tubes is called salpingo-oophorectomy. Oophorectomy and salpingo-oophorectomy are not common forms of birth control in humans; more usual is tubal ligation, in which the Fallopian tubes are blocked but the ovaries remain intact.
In humans, oophorectomy is most usually performed together with a hysterectomy - the removal of the uterus. Its use in a hysterectomy when there are no other health problems is somewhat controversial.
In animals, spaying involves an invasive removal of the ovaries, but rarely has major complications; the superstition that it causes weight gain is not based on fact. Spaying is especially important for certain animals that require the ovum to be released at a certain interval (called estrus or "heat"), such as cats and dogs. If the cell is not released during these animal's heat, it can cause severe medical problems that can be averted by spaying or partnering the animal with a male.