Are there standard dictionaries for Chinese?
Yes. For Mandarin (Simplified Chinese):

The Contemporary Chinese Dictionary (现代汉语词典): This one is for words and phrases. They have a version in both Chinese and English.

Xinhua Dictionary (新华字典): this is for Chinese characters. Also available in both English and Chinese. 

I'm not too familiar with traditional dictionaries. But 國語日報辭典 seems pretty popular from googling around.