Not to repeat what has already been said in numerous threads on this subject already ("Search" is your friend), but the issue turns on IRS rules for valuation of a contribution for deduction purposes.

For items not held for investment purposes for over one year, the general rule is you can deduct the fair market value, but not more than your "basis". Basis is usually what you paid for the item -- e.g., you donate an old personal computer, you can deduct the fair market vaue, but not more than what you paid for the computer when you got it plus any repairs/upgrades. (Special rules apply if you got the computer as a gift -- generally you get the same "basis" as the donor had, so in that case what the person who gave you the gift paid for it.) Not normally a problem, since in general things decline in value as they are used, so "fair market value" is usually less than your "basis".

Special rules apply for things held as an investment (stocks, bonds), real estate (your house), antiques, art, and collectables if they've been held for over a year.

Hard to think of miles as an "investment" since they don't earn interest or otherwise appreciate in value over time, so usually the amount you can deduct when donating miles (or things bought with miles) is the cost you paid for the miles. If you bought the miles from the airline, you have a cost; similarly if you won them in a sweepstakes or received them as interest on a bank account and paid the Federal income tax on them, your cost could be the tax plus whatever you paid to enter the sweepstakes.

The problem comes in if you got the miles as a bonus for signing up for a credit card or for flying. What did they "cost" you? The argument usually is that they didn't "cost" you anything since you didn't pay anything extra to get the miles (the plane ticket costs the same whether you collect the miles or not). To the extent you see them as a rebate (repayment of part of the cost you paid for the ticket -- if *you* paid for the ticket), rebates are not considered income but rather a return of part of what you paid for the underlying item, so there is no "cost" and therefore no "basis".

It gets more complicated if the underlying activity (flight, hotel room, etc.) was paid for by an employer. As dhuey notes, the IRS has issued a statement that they will not consider your personal use of those miles to be "income" from your employment, and thus you don't have to declare the value of those miles and pay income tax on them. Technically, then, they didn't "cost" you anything out of pocket and thus arguably have no "basis".

One other consideration -- the statement by the IRS saying that personal use of the miles need not be reported as "income" from employment contains a caveat: if you convert the miles to cash or cash equivalents, then the statement does not apply. So, if you sold the miles, it would seem you'd have to declare the money you got as being income from your employment. What effect does this have when you donate the miles and take a deduction for them thereby lowering your tax payment? Is the tax savings a conversion of the miles to the cash you didn't have to pay in taxes due to the deduction? If so, must you now declare that as income?

So, it can get rather complicated, and as dhuey notes, the IRS has not issued definitive guidance as to some of these issues. As dhuey also notes, this has been discussed in much greater detail in other threads.

And finally, the discussions do not always result in agreement. And for the record, I do not agree with everything dhuey has said, but then reasonable men may reasonably differ. That's what makes horse races and lawsuits.