From experience, I can say that even if it isn't cheaper than flying, it's definitely less convenient. Amsterdam and Paris are close and popular so the trains run well, but try Echt (NL) and Meckenheim (GER) by public transport. Or Echt to Modane (FR). As soon as you cross borders it's a nightmare.
The German trains website (db.de) does a surprisingly good job (after recently having a terrible experience with Belgian and, three years ago, French public transport websites) of piecing together connections, but that also means it'll happily tell you go take a bus, e.g.: bus-train-train-bus-train-train.
The German trains website (db.de) does a surprisingly good job (after recently having a terrible experience with Belgian and, three years ago, French public transport websites) of piecing together connections, but that also means it'll happily tell you go take a bus, e.g.: bus-train-train-bus-train-train.