The Rongai, Lemosho, and Machame routes are camping routes that take longer and are considered more scenic than the Marangu. On the Marangu route you will be staying in huts as opposed to camping, and you hike up and down the same path.
The Rongai route takes you up the north side of the mountain and you descend down the Marangu route. The Lemosho and the Machame routes traverse the mountain and descends down the Mweka route.