If you swing it right you can get a "Delta" flight that is actually on Lufthansa planes with Lufthansa crews. Only to Europe of course.
Oddly enough the worst flight I've ever been on was a Lufthansa flight from Frankfurt to Seattle. It was booked as a United or some other US carrier, but provided by Lufthansa. Service was horrible, the beer was American swill, only a few of the bathrooms worked.
Probably my favourite carrier would be KLM, but it's been 20+ years and I don't know how they are now. The best recent carrier I've been on was Air China, the plane was a bit older, but the service was outstanding.