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.
Here is a list of the most common Mandarin words, as opposed to individual characters. Some of the entries are individual characters, but the majority are character compounds which form Mandarin words. Adapted from the Steering Committee of the Test of Proficiency - Huayu
ma
Traditional: 嗎
Simplified: 吗
Pinyin: ma
Meaning: (question tag)
māma
Traditional: 媽媽
Simplified: 妈妈
Pinyin: māma
Meaning: mama; mommy
mă
Traditional: 馬
Simplified: 马
Pinyin: mă
Meaning: horse; horse chess piece; Surname
măshàng
Traditional: 馬上
Simplified: 马上
Pinyin: măshàng
Meaning: at once; right away; immediately
máfán
Traditional: 麻煩
Simplified: 麻烦
Pinyin: máfán
Meaning: trouble; troublesome
măi
Traditional: 買
Simplified: 买
Pinyin: măi
Meaning: buy
mài
Traditional: 賣
Simplified: 卖
Pinyin: mài
Meaning: to sell
màn
Traditional: 慢
Simplified: 慢
Pinyin: màn
Meaning: slow
mànmàn
Traditional: 慢慢
Simplified: 慢慢
Pinyin: mànmàn
Meaning: boundless (place); long and slow (time)
máng
Traditional: 忙
Simplified: 忙
Pinyin: máng
Meaning: busy
