Timbuktu has three of the oldest mosques in West Africa. While not as visually stunning as some in Mali, they're still extremely impressive and represent classic and well-preserved examples of the Sudanese style of architecture which prevails throughout much of the Sahel. The oldest, dating from the early 14th century, is Dyingerey Ber Mosque.
You can go into this mosque, west of Place de l'Indépendance, but sometimes only with a guide. The interior is a forest of 100 sturdy pillars, and there are a series of interconnecting rooms with holes in the wall at ground level - in the days before microphones, worshippers who could not hear the imam could look through into the main prayer hall to see when to pray. There's a separate women's section, from close to which stairs lead up onto the roof (ask permission before climbing up) for good views over the town and out towards the desert; don't point your camera south as there is a police building in the vicinity. The muezzin still climbs to the summit of the pyramidal minaret, with its wooden struts, to call the faithful to prayer on those days when the electricity isn't working; otherwise it's done by microphone.