The massive flat-topped mountain that dominates the skyline directly above Rum village is Jabal Ram, and it looms over everything. From the village, it looks sheer and unclimbable, but a route exists up the back side that experienced hikers can manage with a Bedouin guide.
The ascent takes four to six hours and involves sustained scrambling over exposed rock. This is a serious mountain day, not a casual walk, and the route is unmarked. Your guide will lead you through narrow chimneys and across ledges that would be intimidating without someone who knows every handhold. The summit plateau is surprisingly flat and wide, with views that stretch across the entire Wadi Rum basin.
Most visitors are content to admire Jabal Ram from below, and it does make a spectacular backdrop to the village — particularly at sunset, when the west face catches the last light and turns a deep, glowing red. But if you are fit, experienced, and have a good guide, the climb is one of the most rewarding things you can do in Jordan.