I agree with ZhangtheGreat. I can recall only two usages of 的 without deep consideration------possession and adjective. In the usage of possession, I think 的 can be omitted only when it refers to person or administrative unit. The former one like:我妈， 我哥，我女朋友 etc. The latter one like:我国，我省，我单位(the department I work for) etc. Generally we omit 的 when we refer to people who are close to us. The second usage of 的 is adjective. Such as 漂亮的，有用的，讳莫如深的 etc. In your example "有些人知道很多很多，但却不知道最有用的东西是什么", you have already noticed that you can't add 的 after 什么, because it's not supposed to express a possession meaning or adjective meaning. In your example "我牛角很长", we know that there are one possession (我的牛角) and one adjective（很长的）in this sentence. So following the rule I advanced before, you need to add 的 to modify the possession relation. However, we need a further discussion on whether we should add 的 to indicate adjective relation. Actually, if we rephrase this sentence to a complete expression, it should be 我的牛角是很长的. The difference between your sentence and the one I rephrase is whether there is 是 in the sentence. In Chinese, 是 functions as "be". When 是 appears, the adjective follows it must with 的 to indicate this adjective is an adjective. On the contrary, if there is no 是 in the sentence (like your sentence), we can omit 的 behind adjective. For this reason, the correct expression is 我的牛角很长 or 我的牛角是很长的. Hope this helps. : )

In speech, there is no "hard and fast" rule, and many Chinese speakers will include and exclude 的 purely out of habit. If you wanted a very general rule though, it would probably be that 的 can (not must) be omitted when it comes to possessions that you're supposed to have intimate feelings for. Obviously, family is the prime example. When mentioning any family members, 的 can be left out. Places connected to your identity, such as city, country, or various other regions, also qualify. However, when it comes to superficial possessions, 的 is less likely to be omitted. Native speakers will stil understand you if you leave it out, but you would probably sound more odd to them. I hope this helps. Please let me know if you have anymore questions.

1. 这是我妈妈。 这是我的妈妈。我国家好热。 我的国家好热。Both "的" are optional in spoken Chinese but in written Chinese, the second one should be 我的国家. 2. “必不可少的” is one word "indispensable". That's why "的“ cannot be omitted here. "最有用的" is the same. 3. we don't put "的" after "什么" except “干什么的”（what is it used for? or what do you do?）or "什么做的" （what is it made of?）or "什么味的" （what is the flavor?）...... 4. "我牛角很长" and "我的牛角很长" are both ambiguous because if you say so, i will think you, yourself, are a cow and your horns are long. so it's better to say 我的牛的角很长，which means I have a cow and its horns are long. In one word, normally, if there is no ambiguity, 的 is optional but if 的 is part of a word (like必不可少的，最有用的), it cannot be omitted.

In addition, in titles, poetry 的 can be omitted. it would be better to leave it out... 松鼠食物 二人世界 天下英雄好漢 Having too many 的. 我的媽媽的屋子的北方的山頂的古廟的池塘有條怪魚 -> 我媽媽屋子北方山頂古廟地塘有條怪魚 or you can add one to any of the places in this crafted sentence. Also 這是我的媽媽 and 這是我媽媽的 are two different things!

It's really hard to tell when 的 can be omitted. Usually when a noun is polished by a series of adjective words（more than one adj.s）, 的 can't be omitted. per esempio: 我昨天读了（一本）（关于西班牙北部Bilbao）的 书。 奶茶是(草原家庭)(日常生活)和(招待客人)(必不可少) 的 饮品。 -----------This is because when the adj part is too long, these restrictive words are likely to be very important. Therefore, 的 is not recommended to omit. As for short sentences, I think when the adj. part is highlighted, you can put a 的. 这是我妈妈。 --- you may introduce your mother to your friends for example. [Mother is the key word] 这是我的妈妈, (不是你妈)。 --- （这是我妈，不是你妈！- better ） You may stress that This is MY MOTHER, not Yours. 这是我的玩具，不给你玩。 --- This is MY toys! I won't share with you! (This is more common that last sentence...) [MY is keyword] 我国家好热。 --- ! Since you 've used 好 instead of 非常，this can't be written in a formal essay. 【 我们家那边（儿）非常热。 is recommended or to say : (a country o area maybe) 很热。(我国家好热/很热 are a bit weird) 】 有些人知道很多东西，但却不知道最有用的是什么。 --- no 的 after 什么， because it's a pronoun, not a adj here. =Someone may know lots of things, but he doesn't know [ what ] is the most important. 我牛角很长。 --- said by a cow/ox? both with or without a 的 are all ok. It's really hard to grasp the usage of 的，especially, I think, there's not a concrete rule of it. Anyway, when you'd like to highlight a restrictive part, put a 的 in the end. -------------------------- Ciao