There are many Mandarin frequency lists which show the relative frequency of Chinese characters. For example, the Chinese Text Computing web page has several lists of Chinese characters compiled from various sources.
However, Chinese words are often composed of more than one character, so lists of single characters can be deceiving.
The list below shows the most common Mandarin words, as opposed to individual characters. Some of the entries are indivudual characters, but the majority are character compounds which form Mandarin words. Adapted from the Steering Committee of the Test of Proficiency - Huayu
Meaning: Interjection showing surprise, doubt, approval, or consent. Can be pronounced in any of the four tones.
Pinyin: ā yí
Meaning: to love; affection; to be fond of; to like
Meaning: an interjection; hey
Meaning: short (not tall)
Pinyin: ān jìng
Meaning: quiet; peaceful; calm
Pinyin: ān pái
Meaning: to arrange; to plan; to set up
Pinyin: ān quán
Meaning: safe; secure; safety; security
Meaning: (modal particle indicating polite suggestion); ...right?; ...OK?
Pinyin: bà ba
Meaning: (informal) father