Why do English speakers put the word "of" into "I think OF him"?

I find it interesting that native English speakers add the words "with me" or "on me" when starting something like "I have some money". In Japanese we do not say these words when we want to say "I have some money". For example, we just say "お金がある" (okane ga aru) or "お金をもっている"(Okane wo motteiru)　when we want to pay for our own food at restaurant. Both of them can be translated literaly into "I have some money", so the words "with me" or "on me" are not included.

I think that in the English language it's common to add words after verbs like "with me" in the sentence "I have some money -with me". Also, we don't understand why, in English, the word "Of" is added into the phrase "I think OF him". We just accept it but we don't really know why.

I suppose if you just say the words "I think him" then you would feel as if the sentence is incomplete. English speakers say things like "I think him a good person" or "I think he is a good person" it seems that people have the need to add words after the word "Think". So, I think saying "I think him" would sound strange to a native speaker. But if the "Of" is introduced to the sentence, then it doesn't mean like "I think him a good person" but it just means "I think of him". So native English speakers introduce the word "Of" into a sentence to express that you are thinking about them.

In Japanese we say "彼を思う(kare wo omou)" in place of "I think of him". If we translate it into English literally as a word for word translation, it would be "I think you". So Japanese people have a hard time understanding why the words "With me" or "Of" are included into these phrases.

I suppose we can understand beter if we think within ourselves as to why these words are added. In fact that adding words in like "Of" means you have feelings for the person. Or that you truely are thinking what you are saying. The sentence wouldn't make sense to just say "I think him" or it would be thoughtless.

(This essay is the corrected version of my diary which is in "lang-8". http://lang-8.com/73855/journals/231594

A native speaker Mr.AzumiRM kindly corrected it and teach me those right answers for my question about the word "Of" in the sentence "I think of him". So I just have written the corrected sentences by him and his answers into this essay.)