That is an awkward word because it may be one of three parts of speech — a conjunction, a relative pronoun, and a demonstrative pronoun. "I think that the paper that he wants is that one" illustrates the three in the order given. More than one modern writer has tried the experiment of spelling the word differently (that and thatt) according to its function; but not all readers are likely to find this expedient helpful, and any official who used it would be likely to get into trouble.
It is a sound rule that that should be dispensed with whenever this can be done without loss of clarity or dignity. For instance the sentence just given might be written with only one that instead of three: "I think the paper he wants is that one". Some verbs seem to need a conjunctive that after them more than others do. Think is one that can generally do without. The more formal words like state and assert cannot. As to the omission of the relative that, see Which And That.
The conjunctive that often leads writers into error, especially in long sentences. This is not so much a matter of rule as of being careful. Here are some examples:
It was agreed that, since suitable accommodation was now available in a convenient position, and that a move to larger offices was therefore feasible, Treasury sanction should be sought for acquiring, them.
Here a superfluous that has slipped into the middle of the sentence. The first that was capable of doing all the work.
All removing residential subscribers are required to sign the special condition, that if called upon to share your line that you will do so.
That is another case of careless duplication.
As stated by the Minister of Fuel and Power on the 8th April, a standard ration will be available for use from 1st June, 1948, in every private car and motor-cycle currently licensed and that an amount equivalent to the standard ration will be deducted . . .
The draftsman of this forgot how he had begun his sentence. He continued it as though he had begun "The Minister of Fuel and Power stated . . . " instead of "As stated by the Minister of Fuel and Power". The consequence was that he put in a that which defies both sense and grammar.
Their intention was probably to remove from the mind of the native that he was in any way bound to work, and that the government would protect him from bad employers.
This example shows the need of care in sentences in which that has to be repeated. If you do not remember what words introduced the first that, you may easily find yourself; as here, saying the opposite of what you mean. What this writer meant to say was that the intention was to remove the first idea from the native's mind and to put the second into it, not, as he has accidentally said, to remove both.
It is good idiom, though not always elegant, to use the relative that as equivalent to which with a preposition, as in:
During the two years that these works are under construction (during which).
Owing to the pace that the car was going . . . (at which).