The international bus station handles traffic to Sust in Pakistan, as well as two different routes into Kyrgyzstan. Note that you’re charged excess baggage rates for every kilo over 20kg on international buses.
The road to Kyrgyzstan
The 720km-long road due north from Kashgar via the Torugart Pass to Bishkek in Kyrgyzstan has been open to Westerners since the 1990s, though this trip is complicated by the fact that foreign travellers are not allowed through the border in either direction on public transport, and must be delivered and met by official guides. While, in theory, the border crossing is open Mon–Fri, 10am–5pm, in practice you need to cross before noon and be prepared for sudden closure of the border post for national holidays, bad weather (the pass lies at 3750m and snow is frequent even in summer) and random political reasons. You’ll have to organize the trip though an agent in Kashgar or Bishkek and expect to pay upward of US$200 per car from Kashgar to the border, and US$150 per car for onward transport to Bishkek.
An alternative, and easier, option is to head across the southern Irkeshtam Pass, 210km west of Kashgar, by bus (currently Mon and Thurs; US$50), heading on to the southern Kyrgyz city of Osh on a rough road. This route has become popular with cyclists; although there are five major 2400m-plus climbs before the border, there are petrol stations about every 40km for water, and towns or villages no more than 65km apart. Note that Osh was the scene of inter-ethnic riots in 2010; check the current situation before heading this way.
Whichever way you take to Kyrgyzstan, check and double-check the visa requirements in advance before you rely on getting a visa on arrival; in China, you can do this at the Kyrgyz embassy in Beijing or the consulate in Ürümqi.
The road to Pakistan
The fabled Karakoram Highway heads from Xinjiang to Pakistan over the Khunjerab Pass. It would be a shame to do this all in one go, but there are direct buses – in theory every day, in practice whenever there are enough people – from Kashgar to the Pakistani city of Sust (¥290). It may make more sense to go to Tashkurgan and take the bus from there, as there are occasional buses from Tashkurgan to Sust and all the Kashgar buses stop in Tashkurgan anyway. Despite the gradient (the pass tops out at 4693m), this route is popular with bikers and cyclists. Note that the border is only open from May 1 until October (the exact closure date varies), and third-party nationals will need to have organized their visa in advance, something usually only possible in their home country.