Unlike airports, train stations are usually located in the heart of the city, thereby eliminating the need for transportation to and from downtown. In fact, many high speed trains can actually get you from a hotel in one city to a hotel in another city faster than an airplane if the distance is between 250-300 miles. You keep your luggage with you in most cases, eliminating the possibility of it becoming lost in transit or having to worry about check-in requirements or baggage waits. You don't have to worry about missing the scenery, because it passes right in front of you. You can get on and off wherever the train stops - change your itinerary at the spur of the moment (it's a little difficult to do that once your flight has taken off). Train travel is almost never delayed by weather conditions, as happens frequently with both airplanes and automobiles. You don't get stuck in traffic on trains, nor do you have to worry about flat tires, unfamiliar traffic laws, maneuvering through and mastering congested arteries in foreign cities - all of the expenses and inconveniences connected with airplane and automobile travel.
On a train you can read, sleep, eat, drink, flirt or take a walk. Trains give you an opportunity to meet a wide variety of people - those native to the country you're traveling in and people like yourself who are on their way to somewhere new. I shared Bulgarian chocolates with a Norwegian biker on his way home from an extensive bike tour of Eastern Europe, aboard a train from Copenhagen to Oslo; argued with two men as we headed to Barcelona that I was, indeed, American - they insisted that all Americans were fat and blond, two attributes that I lack; I discussed American politics and racism with a Finnish woman as we headed above the Arctic Circle; I shared a lunch of bread, cheese, yogurt and fruit with an Australian diplomat en route to Nice; I've collected scraps of paper with names and addresses, business cards, made dates, met future lovers, discussed politics and poetry - in short, train travel afforded me the luxury of experiencing new faces from all walks of life and a kaleidoscope of nations.
