F. Scott Fitzgerald may have summed up its drawback most succinctly in his admonishment: “An exclamation mark is like laughing at your own joke." And who wants to be that sort of writer?
The exclamation mark is often the lazy writer's way of conveying emotion. By using it, you're telling the reader how to interpret the line. “Pay attention," you say to the reader, “this is going to be exciting." Instead of relying on this rascal of punctuation, you should choose your words precisely so that they carry the emphasis themselves. Focus on using vivid and striking nouns and verbs that capture the essence of the strong emotion you want to convey.
Instead of this:
The man came right at him, ready to strike!
You might write this:
The man lunged, his right arm cocked, hand fisted.
The urgency of the moment comes through the image of the man about ready to strike, and the energy of the verbs: lunged, cocked, and fisted. And that approach does a more convincing job than the slim exclamation mark.
Of course, exclamation marks aren't—and shouldn't—be obsolete. Writers can use them to create a specific impact. For example, Thom Jones used exclamation marks in his short story “I Want to Live!" to mirror the rush and abrupt shifts that come with direct thought. The story is told from the perspective of a woman dying of cancer. This passage comes after a chemotherapy treatment:
The third treatment—oh, damn! The whole scenario had been underplayed. Those movie stars who got it and wrote books about it were stoics, valiant warriors compared to her. She had no idea anything could be so horrible. Starving in Bangladesh? No problem, I'll trade. Here's my MasterCard and the keys to the Buick—I'll pull a rickshaw, anything! Anything but this. HIV-positive? Why just sign right here on the dotted line and you've got a deal! I'll trade with anybody! Anybody.
While you might not need to limit yourself to the ration of three exclamation marks in a lifetime that editor and writer William Maxwell advised, you should use them sparingly and with good reason.