I recently got an American express gift card for my birthday. It has a value of $50. Where can I purchase bitcoins (or litecoins) with this giftcard?
http://btcquick.com uses Google Checkout and supports Amex, I have not tried a gift card but it should work.
They do require identity verification to combat the (massive) fraud risk they face.
I gave btcquick a try some time ago but never had any success. Amazon webpay is a simple way to cash-out a gift card. Not really intended to send yourself money though -- the official way to do that would be to have a trusted friend use their amazon account to send it to yours. Or you can figure out some workaround I'm sure. More details at the link.
Pros - no fee.
Cons - takes 5-7 days to get the cash-back into your bank account. Which may be what you're trying to avoid in the first place.
Amex also claims you can redeem their gift cards for cash by calling the number on the back, but I don't know how long that takes; my guess is a check in the usps in 6-8 weeks minus some fee. Not recommended.