You're confusing a lot of things:
You have to pay taxes on any income (meaning incoming money). The only way around paying taxes is if you can get Non-Profit status from the IRS.
So, say you have a web site and you make background images. You can share these images for free, and ask for "donations". These donations are INCOME. dont let the term donation and donation to a non profit confuse you.
Frank's answer is not correct: true donations are not income.
When something (money or property) is given to an individual with no consideration, it is considered to be a gift. While there is a gift tax, it is a liability of the donor and not the recipient. And since the gift tax only kicks in at $13K/recipient/year**, it likely wouldn't even apply.
Just keep in mind the "no consideration" part. If you give anything of value in exchange for a donation, it becomes a purchase... which is subject to income tax.
** Some gifts don't trigger the gift tax (spousal gifts, paying for tuition, etc), and some gifts are tax deductable (gifts to non-profits).