There's nothing wrong with adding "personality" to your website. But if you're like most small business owners, your website has a job to do—grow your business. Don't get in its way or spend effort on things that don't help it achieve that goal! How does your website grow your business? By solving your customers' problems and getting them to trust you enough to give you their time or money.
Trust and Credibility
Some websites need to be "fun" because that's what their target audience is looking for. But every business website needs to be professional—even fun ones. A professional image lends credibility to everything you proclaim on your website. It's all strangers have to go by.
How to You Detect an Unprofessional Website?
By comparison to other websites that are considered professional. And the more web-savvy the user, the more they can tell. What are the signs? Let me put the question back to you. Have you ever seen an unprofessional-looking...
...business card?
...print ad?
...TV commercial?
How could you tell? Over-used clip-art graphics. Graphics or text that don't relate to the business. Obvious advertising "tricks". Elablorate, hard-to-read fonts. Too many colors. Too cutesy. Too trite. Too many exclamation points. Etc., etc.
Bottom Line
If you're seriously looking to grow your small business, remember that your business website is not built for your personal enjoyment. That's what personal websites are for. If you're really not all that interested in making a profit, I would (as would the IRS) classify your business as a "hobby".