No, but you do need to keep track of how much they were worth when you bought them. Then, once you sell them or trade them for goods or services, you pay taxes on the profit.
So, for example, if you bought BTC at $400, then sold them at $450, you pay tax on the $50 difference, because you made a profit.
If you lost money in the transaction, there is no profit, there fore there is no tax. This is because BTC is treated as property, not currency.
If the transaction is under $600 they do not care about the tax.
The whole rule set is pretty short, it sounds like they did not know how to proceed with BTC and threw something together quickly.
This all assumes that you wish to operate within existing tax law. BTC of course makes operating outside the tax system very easy, that is an ethical choice you need to make for yourself.
If you wish to get out of fiat, and never report anything after the purchase, but you still feel obligated to pay taxes, you could pay the tax on the full purchase price and then be done with it, but that again is an ethical choice. Bitcoins, when used correctly with TOR and purchased without a paper trail in cash, are for practical purposes untraceable. Whether to engage with the tax system at that point is purely an ethical matter, since you have no reasonable expectation of getting caught.
We all know there is a lot of corruption in government, and much of your tax dollars are probably wasted outright, or spent on things with which you disagree. However, our taxes fund everything from the roads we drive on to the parks we use, to the retirement check you will get, to the underfunded schools which we use to educate children.
Sort that out within your own mind. Up to you.
1This answer needs an update now that the IRS rules have changed in 2018. – Josephzzz – 2018-03-26T18:59:00.767
@JoseCifuentes I don't think there's any change that affects this answer. Am I missing something? – David Schwartz – 2018-04-04T02:31:48.640
I read this post from Turbotax: https://ttlc.intuit.com/questions/4138638-how-do-i-report-cryptocurrency-mining-income It looks like the simple action of mining is a taxable event, even if you don't sell and just hold the coins. For example, if I mine throughout the year and hold, I still have to pay taxes for that year based on the coin prices on the dates they were mined.
– Josephzzz – 2018-04-04T13:53:56.327