Technically, this is considered "income" for you, and is actually not considered a "donation" for your donors, but is instead a "gift" (not tax-deductible for your donors). So, you are technically required to report it, and there is a pretty significant audit trail that can be followed to prove you made that money. I don't know if PayPal is required to file 1099s for payments received, but if you've ever received such a document, so has the IRS, and they'll match it to the income you claimed and see a discrepancy, triggering an audit. Depending on the amount that it affects your taxes (it can be significant; if you have a $50k/yr day job, you'd owe the government 25 cents on every dollar donated), they can let it slide, they may simply dock your next return, or they may come after you for interest and penalties or even charge you with criminal tax fraud if they could prove you maliciously attempted to conceal this revenue.
Now, if you already itemize using a Schedule A, then you can erase this income by deducting the costs of the server, not to exceed the amount of the donations. The best you can do is offset it; you cannot use this deduction to reduce taxable income from other sources. Also, you must itemize; you can't take your standard deduction, and with a maximum possible deduction of the actual costs of running the server ($1500, IF you receive enough donations to fully pay for it) compared to one person's standard deduction ($5800), you'll want to take the standard deduction if you don't have other significant deductions (medical expenses, mortgage interest/property taxes, etc).
If you were charging users a monthly fee for use of the server, then you've basically created a de facto sole proprietorship, and you would still have to count the fees as income, but could then deduct the full cost of running the server. You'd fill out a Schedule C listing the revenue and expenses, and back them up with statements from your ISP/hosting company and from PayPal. Now, this would apply if you were running the server with the primary goal of making a regular profit; Schedule C cannot be used for income from a "hobby", undertaken primarily for enjoyment and where a few bucks in revenue is gravy. Whether you think you can get away with that in your current situation is your prerogative; I don't think you would, given that the donations are solicited and optional, and thus there is no expectation of ever turning a profit on this game server.