I'm developing a website:
My customer wrote the following in the front page:
Hi, I’m Brian “Funshine” Alexander. I offer professional Music, Voices, and Shows for kids and adults! SCROLL DOWN HERE FOR MY DEMOS!!
Does it look unprofessional?
That depends on how you want to present yourself to your audience. If you want to appeal to the 4chan crowd or put yourself on a par with, say, the local used-car dealer, by all means stuff your prose with bundles of exclamation marks.
But you have to ask yourself if exclamation marks (especially multiples) are really doing anything to help you. For every 4chan devotee who thinks nothing of the excess, there are plenty who will be put off by this forced display of artificial enthusiasm.
The fact is, exclamation marks are seldom needed, especially in ordinary, informational prose.
I once had a junior copywriter working for me who had a proclivity for using slammers (slang for "exclamation points" or "exclamation marks") in her writing. I sat down with her one day and gave her a five-dollar bill. "New rule," I said. "Every time you use a slammer you owe me a buck. The first five are on me." She pinned the bill to her bulletin board. When she and her husband moved across the country several years later, she returned it to me unspent. Her writing, I might add, was much improved, and she thanked me for the lesson. Her portfolio was good enough by that time to get her a senior copywriter position at a large agency in her new city.
Yes, it is absolutely unprofessional.
I won't say it's never effective, but that's not what you asked. Professional design avoids those devices - for several good reasons, some mentioned in other answers, but give special attention to this one: unprofessional advertising overuses CAPS and exclamation marks to a ridiculous extent. Why let yourself be associated with that?
Robusto makes a good point about knowing your audience. Beyond that, I think caps and exclamation points are used for emphasis and attention. Try to find other ways to accomplish those goals. Spacing? color? italics? placement?