Many credit/charge* cards accrue bonus points that can be exchanged for gifts, gift cards, cash, etc. Many of these cards also offer the chance to change these points in for a charitable contribution to any charity of your choice. Often, the exchange value for such contributions is better than the exchange value for cash or goods.

You don't get to deduct this kind of contribution from your taxes, though, because the points were never realized by you as anything tangible. The bank behind the card actually gets the deduction in this case. However, given the disparity between the exchange value of the points (between goods/cash and as a charitable contribution), you may still come out ahead by donating your points even without the tax deduction. (This is true for Amex charge card points.)

Another option is donating real money (not points) through your credit/charge card. In this case, it's your money you're donating, so you get the tax deduction. You also tend to earn points since it's real money you're spending. With at least some cards, you can donate money through the card without the charity having to take credit cards. The bank will issue a check in the amount you donate (less fees) to the charity. Since the charity is not taking the credit card transaction, the bank is not taking in the vendor fees for such a transaction. As such, the bank will tend to charge a fee for this kind of donation. For Amex (all I've researched so far), it's 2.5%. You're unlikely to earn as much in points as you pay in the fee, though. You can deduct the donated amount, but not the fee. In such instances, it's better to simply write the check, of course, but going through a credit/charge card provides an opportunity for a regular donation schedule. For example, you can set up your Amex to send $100 each month to a charity of your choice. (It'll cost you an extra $2.50 each month in transaction fees.) The convenience of such regular giving may be worth the nominal fee to you, especially since it requires none of your time past the initial setup.

Disclaimer 1: I ain't no tax dude, so don't take my word for it.

Disclaimer 2: I ain't no lawyer, either, so these disclaimers may not be construed as legal advice.

*A credit card is basically a charge card that can carry a balance more or less indefinitely. A charge card is one that is paid off in full at the end of each month. Charge cards also usually come with annual fees; without balances, there usually isn't any interest, though. Whether a card is a charge card or credit card is defined by the type of card (i.e., by the issuing bank), not how it's used by the consumer. As far as I know, only Amex still offers charge cards (e.g., their green card), but Amex also offers credit cards now.