At the moment it is not recomended to visit Mosul, or any other part of Iraq, as a tourist due to the ongoing conflict.
All flights arrive at Mosul International Airport IATA: OSM, the international traffic is however limited to flight connections with Dubai and Istanbul. Overland travel is possible, Mosul is along Highway 1 & 2 but can be quite dangerous with sporradic attacks on vehicles travelling along the roads. It will also take a long time due to numerous traffic checks. A night train from Gaziantep started running in eary 2010 but is now cancelled until further notice. Services linking Baghdad with Mosul are supposed to start "soon".