Sometimes called the exclamation mark, the exclamation point is used at the end of a sentence or after an interjection to show strong emotion or emphasis.

Exclamatory sentence: The rain did not stop for four days!
Strong command: Be back at ten o’clock or else!

Interjection: Wow!

When an emphatic interjection or direct address begins a sentence, you may use an exclamation point or a comma, depending on how much you want to show the strong emotion.

Correct: No, I don’t want to go there.
Correct, more emotion: No, I don’t want to go there!

Correct, even more emphasis: No! I don’t want to go there!

Beware of overusing exclamation points. Using them too frequently makes them less meaningful.

Use of an exclamation point inside parentheses is used by some to show irony.

Usually, the ironic tone should be clear from the words, but sometimes this special punctuation is added for emphasis. Some authorities do not consider this construction necessary, and it is of very limited use in most standard English writing.

OK, informal: That butcher (!) is a vegetarian.
(The punctuation is probably not necessary, but it was placed there to emphasize the irony.)