Domestically, you can fly to Urumqi from virtually everywhere.
New international flights are constantly being proposed (though not necessarily finalised). You can fly to Urumqi from a number of Central Asian cities, including Almaty (Kazakhstan), Bishkek and Osh (Kyrgyzstan), Islamabad (Pakistan, via Kashgar), Novosibirsk (Russia), Moscow, Baku (Azerbaijan) and Tashkent (Uzbekistan). There’s also continued talk of new flights to Lahore (Pakistan) and Punjab (India); seasonal flights go to Seoul. Linking Tashkent and Lahore with Kashgar has been debated forever.
There are overland border crossings with Pakistan (Khunjerab Pass), Kyrgyzstan (Irkeshtam and Torugart Passes) and Kazakhstan (Korgas, Alashankǒu, Tachéng and Jimunai). Apart from Alashankǒu, China’s rail link with Kazakhstan, all of these borders crossings are by bus, though you can generally get a bike over.
Remember that borders open and close frequently due to changes in government policy; additionally, many are only open when the weather permits. It’s always best to check with the Public Security Bureau in Urumqi for the official line, or Lonely Planet’s Thorn Tree to see what other travellers are saying. A new crossing, the Kulma Pass to Tajikistan, may open to foreign travel in the coming years.
Heading back into China, the obvious route is the train running through Gansu. More rugged approaches are along the southern Silk Road from Charklik to Qinghai, and Karghilik to Ali (Tibet).