Living abroad I do have both, the DKB card/account as well as the gebuhrenfrei Mastercard. Both have advantages and disadvantages but seem to be the two best offers in Germany.

The DKB card allows you, as been said, to withdraw money from any ATM anywhere without a fee. If the machine itself adds a fee (as ATMs in the US do) you can hand in the receipt to DKB and will be reimbursed. However if you pay with the DKB card in other currencies than EUR you will be charged a 1,75% fee on top of your purchase. Note that DKB not only has their own VISA but also hosts the Germanwings Mastercard, the HHonors card as well as the German LH M&M cards. Conditions vary from card to card, be careful which one fits your needs best.

The gebuhrenfrei card does not have a fee for paying in non-EUR currencies, however it is not to be recommended for cash withdrawals (they charge interest from the moment you take the money out of the ATM). Furthermore you have to actively settle the bill by transferring money to Advanzia bank (the company behind the gebuhrenfrei card) - if you forget to transfer at least the minimum amount it will result in a hefty 10 EUR charge. Simple solution: Don't forget to pay your bills.

For obvious reasons I have both cards: One for cash withdrawals and one for payments. I have good experiences with both banks and their customer services and can recommend both.

If anyone is interested in opening a DKB account I'd be happy to refer someone through the "Kunden werben Kunden" program. Also if someone wants to get a LH M&M credit card I would be a happy sponsor (getting me 10000 award miles and the sponsoree whatever miles applicable for their card) and would in exchange offer this person to be my sponsor for my new LH SEN credit card (getting this person 10000 award miles), to make sure we both benefit from that deal.