Sometimes to learn about something new it is good to look at the extremes of it. To get an insight on the various forms of chinese characters I want to show the different characteristics and compare.

I might extend the list once I found something new and interesting. Sources are added in the form of [1].

Frequency

Frequency of a character depends on the point of view. But as we don't want to satisfy any scientific requirements we can be a bit imprecise on that. I rather hope to focus on a few examples.

Most frequent character

A way of getting the most frequent character is to start a statistical evaluation on a text corpus. Somebody already did that, and wrote about how it technically works and which sources were used. You see that there basically exist two differnt evaluations: one for Modern Chinese, one for Classical Chinese.

• According to the statistics for Modern Chinese
  
  的

  is the most frequent character with about 4% of use.
  This word is a possessive particle and can be used like 我的书, wǒ de shū, "my book" (literally: "I particle book").

• But for Classical Chinese
  
  之

  is the most frequent one with about 1% of use. 不 has nearly the same frequency. In Classical Chinese 之 is partly used where 的 would be used in Modern Chinese, so both statistics seem to show the same result (more on it's usage).

What is 4%?

To have a quick look on how much 4% actually is, here's a chinese phrase. It is taken from [2], there are 3 occurences of 的 in 69 characters (not counting typhographic chars and arabic numerals), which is about 4%:
“中國”一詞自古有之，最早指居於“天下”（古人对世界的称谓）中心的中原地帶；在近代以来，特别是1912年中华民国成立后，“中國”一詞始成爲民族國家意義上的法律和政治概念。

Interestingly the most frequent 6 characters in Modern Chinese sum up to 10% where as it needs the 12 most frequent characters in Classical Chinese to make up nearly the same amount.

Least frequent character

Again, it depends on the criterion which character is least frequent. But as we are working on examples we can overlook that.
The Chinese language unlike western languages tended to have a character for every particular thing. I would conclude it's in its nature to have a few characters that are never used except for one thing.

• 壢

  is a character as mentioned above. It's only used in association with 中壢, Zhōnglì, a city in the northwest of Taiwan[1]. As that I think it does qualify for one of the least frequently used characters.

More to come...