In 2014 the IRS announced that it published guidance in Notice 2014-21. In that notice, the answer to the first question describes the general tax treatment of virtual currency:
For federal tax purposes, virtual currency is treated as property. General tax principles applicable to property transactions apply to transactions using virtual currency.
As it's property like any other, capital gains if and when you sell are taxed. As with any capital gains, you're taxed on the "profit" you made, that is the "proceeds" (how much you got when you sold) minus your "basis" (how much you paid to get the property that you sold). Until you sell, it's just an asset (like a house, or a share of stock, or a rare collectible card) that doesn't require any reporting.
If your initial cryptocurrency acquisition was through mining, then this section of that Notice applies:
Q-8: Does a taxpayer who “mines” virtual currency (for example, uses computer resources to validate Bitcoin transactions and maintain the public Bitcoin transaction ledger) realize gross income upon receipt of the virtual currency resulting from those activities?
A-8: Yes, when a taxpayer successfully “mines” virtual currency, the fair market value of the virtual currency as of the date of receipt is includible in gross income. See Publication 525, Taxable and Nontaxable Income, for more information on taxable income.
That is to say, when it was mined the market value of the amount generated should have been included in income (probably on either Line 21 Other Income, or on Schedule C if it's from your own business). At that point, the market value would also qualify as your basis. Though I doubt there'd be a whole lot of enforcement action for not amending your 2011 return to include $0.75. (Technically if you find a dollar bill on the street it should be included in income, but usually the government cares about bigger fish than that.)
It sounds like your basis is close enough to zero that it's not worth trying to calculate a more accurate value. Since your basis couldn't be less than zero, there's no way that using zero as your basis would cause you to pay less tax than you ought, so the government won't have any objections to it.
One thing to be careful of is to document that your holdings qualify for long-term capital gains treatment (held longer than a year) if applicable.
Also, as you're trading in multiple cryptocurrencies, each transaction may count as a "sale" of one kind followed by a "purchase" of the other kind, much like if you traded your Apple stock for Google stock. It's possible that "1031 like kind exchange" rules apply, and in June 2016 the American Institute of CPAs sent a letter asking about it (among other things), but as far as I know there's been no official IRS guidance on the matter. There are also some related questions here; see "Do altcoin trades count as like-kind exchanges?" and "Assuming 1031 Doesn't Apply To Cryptocurrency Trading". But if in fact those exchange rules do not apply and it is just considered a sale followed by a purchase, then you would need to report each exchange as a sale with that asset's basis (probably $0 for the initial one), and proceeds of the fair market value at the time, and then that same value would be the basis of the new asset you're purchasing.
Using a $0 basis is how I treat my bitcoin sales, though I haven't dealt with other cryptocurrencies. As long as all the USD income is being reported when you get USD, I find it unlikely you'll run into a lot of trouble, even if you technically were supposed to report the individual transactions when they happened. Though, I'm not in charge of IRS enforcement, and I'm not aware of any high-profile cases, so it's hard to know anything for sure.
Obviously, if there's a lot of money involved, you may want to involve a professional rather than random strangers on the Internet. You could also try contacting the IRS directly, as believe-it-or-not, their job is in fact helping you to comply with the tax laws correctly. Also, there are phone numbers at the end of Notice 2014-21 of people which might be able to provide further guidance, including this statement:
The principal author of this notice is Keith A. Aqui of the Office of Associate Chief Counsel (Income Tax & Accounting). For further information about income tax issues addressed in this notice, please contact Mr. Aqui at (202) 317-4718