There are times when the ear not only guides us through difficult situations but also saves us from minor or major embarrassments of prose.
--From Strunk & White's The Elements of Style
A friend of mine, who speaks English as a second language, once told me that one of her English teachers told her never to use the word that in a sentence.
Granted, that is an overused and generally redundant word. But like most rules of the English language, there are exceptions. Don't follow this rule slavishly.
Here's a tasteless example that you might find in a bad romance novel:
He was worried. He felt that his larger-than-average member, which he knew would impress his date later that night, might not be up to the task.
He was worried. He felt his larger-than-average member, ...
Always re-read your work. Something as minor as the omission of the word that can have dramatic, and potentially embarrassing, results.