Sometimes people get overzealous about deleting every "that" they can find in a sentence. Here's why you need it sometimes.
When "that" introduces a relative clause, it can usually be deleted, provided it’s not the subject of the relative clause. In "the rumor that Fenster heard," we can omit "that" and write "the rumor Fenster heard." On the other hand, if "that" is introducing one of those explanatory clauses, it usually can’t be deleted. If you do, the reader is likely to mistake what follows for a relative clause. If you remove the "that" from our second example, it starts out as "the rumor Fenster started," which sounds just fine—until the clause keeps on going—"the rumor Fenster started dyeing his hair"—and the reader realizes you’re talking not about a rumor started by Fenster, but about a rumor to the effect that Fenster started dyeing his hair. When I read a sentence like that, it wastes my time because I end up re-reading it and mentally inserting the missing "that." It’s another miscue creating a garden-path sentence.
Omitting 'That' After Adjectives
As with verbs and nouns, there are adjectives that tolerate "that"-deletion pretty well, and adjectives that don’t. Common adjectives such as "glad" or "sad" sound fine without a "that": For example, "I’m glad you came," and "we’re sad you’re leaving." But when they’re less common, with a more specific meaning, you’re better off keeping the "that." "She’s furious you never called" would sound better with a "that," and so would "We’re ecstatic you got the job."
Go By Your Ear
If you’re a native English speaker, the main rule to follow here is to go by your ear. You probably know what sounds natural and what doesn’t, and all you need to do is give that native-speaker intuition more weight and authority than a rule stating that you should omit "that" whenever possible.
If you’re not a native speaker, I recommend keeping the "that" unless you’re dealing with a verb, noun, or adjective that you know will sound good without it. It’s safer to leave it in than to leave it out. As you write and read more, you’ll identify more of the words that allow you to omit "that."
This article was written by Neal Whitman, who has a PhD in linguistics, and blogs at literalminded.wordpress.com.