Delta Reserve Credit Card - access to Delta Crown Room Clubs https://www201.americanexpress.com/cards/Applyfservlet?csi=37/21452/b/57
Korean Airlines Visa Signature - 2 free VIP lounge coupons (per year)http://www.skypassvisa.com/cgi_w/cfm/creditcards/korean_air/skypass_signature_splash.cfm?ics_src=55275&redirect=nm201
You can also see which lounges are available via Priority Pass, American Express (Platinum Charge US), Diners Club, Lounge Pass, and on a paid daily membership on the individual program sites or via this tool
You normally get into the lounges by flying lots and getting "status".
However if you are excessively delayed, and smartly dressed+polite, sometimes you can persuade customer services to give you a lounge pass to help you manage the wait.
Either by buying a 1st or business class ticket or being an elite member of their frequent flyer program (usually 50,000 miles a year). Otherwise, sometimes airlines offer reduced prices and sometimes 3rd parties have arrangements with airline lounges, I get Priority Pass Lounge privileges through my bank for example.
Im not too sure about free, but I do know that airlines sell one day passes for pretty cheap - 40-50 bucks maybe.
So if you want to look like you actually belong to the airline's Gold Platinum Super Premium Elite World Traveler Bonanza Club, get the day pass.