I am adding to what StoneyB said in answer to the question, "When can I remove the word “that” in a sentence?" I was asking the same question myself, about when to or not to use "that." The sentences I was unsure of using were "I am sorry that I did not call you," or "I am sorry I did not call you."
While reading StoneyB's response, I was having a hard time absorbing to "parts of speech" terminology. I never did well with that in high school - my solution was to verbalize the sentence in my mind and if it sounded correct, I went with it! This method may work okay for those who have heard and spoken Americanized English for a long time, but is not the best advice for the English Language Learner.
All I have done is to add some of my own personal examples and maybe clarify the parts of speech that StoneyB discussed in his post. I stand to be corrected by anyone, please.
Knowing when or when not to use the word "that" in a sentence when you feel that you use it too often:
Example 1 - "that" - relative pronoun:
"It's the same meatloaf that (used as a relative pronoun) we had yesterday."
You can leave out the "that" in the sentence above because "it acts as the direct object of the verb in the relative clause" (StoneyB, 2014).
Direct object of the verb? - Leave it out.
"It's the same meatloaf we had yesterday." - Correct.
However, if it is used as the ''subject of the verb in the relative clause" (StoneyB, 2014), you could not leave it out:
"It's the same meatloaf that (subject) won (verb) in the cook-off."
Subject of the verb? - Leave it in.
"It's the same meatloaf ___ won in the cook-off." - Not correct.
Example 2 - "that" - subordinating conjunction:
"I am sorry that (used as a subordinator) I did not call you."
That appears in front of the subordinate clause and behind the verb (am), in the main clause.
"I am sorry I did not call you."
Both uses are fine.
Example 3 - "that" - subject of the sentence:
If "that" is the subject of the sentence, it cannot be left out:
"That I am inconsiderate is a matter to be discussed later." - Correct.
Example 4 - "that" - conjunction which does not appear and is not spoken close to the main verb in the sentence:
When the verb in the main clause is separated from the subordinate clause by a lot of other words, such as those used as part of an adverbial phrase, the that must remain for clarity in writing. In spoken English, it may be okay to leave it out, but it sounds a bit lazy to me.
Formal writing: "I am sorry in so, so, very many ways that (still used as a conjunction) I did not call you." - Correct.
Spoken English: "I am sorry in so, so, very many ways I did not call you." - Okay, but awkward.
Example 5 - "that" - predicative complement used with a verb:
Without the predicative complement, the sentence would not tell us much - for example, "Many folks thought," does not stand well on its own, giving very little information about what was thought.
"Many folks thought that my meatloaf was better." - Correct.
"Many folks thought my meatloaf was better." - Okay in speech, but not so good in writing.
English Language Learners Stack Exchange, (2014). When can I remove the word "that" in a sentence? - asked by T2E on May 26, 2013. Answered by StoneyB on May 27, 2013, edited March 7, 2014.
Englishpage, (2015). Forum thread: English Language Questions: Predicative Complement. Asked by Camilus, Member, April 17, 2004. Answered by Pete, Super Moderator, April 19, 2004.