Beside Confucianism, what other way of thinking has had much influence in China?

Ancient China that is(:

Buddhism

I would say Buddhism and Taoism..... but Chinese didn't embrace Buddhism in heart. They just "embrace Buddha's feet in his hour of need", which is a Chinese saying.

Well their is Confucism, and Noe Neo-Confucius. Neo Confucius is different from classical Confucius thought, but the Noe-confucists claim it is the same. Neo Confucius's introduced the classical repressive society that we associate with China.

Another major influence is Daoist thought, and there are 2 schools of this.

Buddhism has an impact, but Chinese Buddhism is a mix of Buddhism and Daoist thought. Tibetan and Nepalise buddhism is somewhat different to that seen in China and Japan.

Western thinking also had a major influence on modern China (the modern period starts in 1901 with the end of the Qing Dynasty). We should not neglect the impact on the way Chinese people are today. Though China doesn't just do things the western way, they have embraced Western Science, Engineering and business concepts.

China also has many Muslims, though in most of China, muslims, Christians and Jews had little impact (in fact Jews in China ate pork). Some parts of China islam has a large impact.

Legalism, the rule of law.

It was started by the first Emperor and has made a come back since Mao was in power.

It hard to explain why, but in a way it is a system that addresses the law of the land that focus on the 'leaders' power and rule on the land.

http://en.wikipedia.org/wiki/Legalism_%28Chinese_philosophy%29

if ancient times: Taoism and Buddhism (not so much now)

if present times: their own thinking