Traveling by train can be a great experience, and it has many advantages. Providing you plan your journey carefully it can be one of the most relaxing and enjoyable means of travel. Although it's by no means as fast as going by plane, traveling on an train often affords you a greater degree of comfort and conveniece.
The comfort can be a huge bonus. Planes are fast, effective ways of getting about, but those airlines sure do cram you in, and leg room is at a real premium. Modern express trains aren't exactly what you'd call roomy, but generally you have more space than you would on a plane, plus it's usually easier to get up and walk around. Trains in most western countries have seats facing each other over tables so its easy to work or play games with your family as you travel.
Cost can also be an advantage of train travel, though not necessarily to the extent you might think. These days, when the airline industry is so competitive, it's actually possible to fly between some destinations more cheaply than it is to take the train. This is especially true in the US and Canada, as well as European countries in which the state has tended to have a hands-off attitude to railways, such as the UK and Switzerland. If you're genuinely undecided about whether to travel by train or plane, don't assume that the railroad track is necessarily the cheapest option. On the other hand what may be the cheapest option - and the one that offers most flexibility - is to make a journey combining plane and train. Say, for example you were traveling from the eastern US to Europe, and you wanted to visit a few different destinations. You could fly direct from JFK to Schipol, Amsterdam. There's a huge train station right under Schipol, so you can board a train and travel down or across Europe, stopping in a number of cities and countries on the way.
One final advantage of the train is sometimes overlooked - train stations tend to be right in the middle of the cities they serve, unlike airports which for very practical reasons are usually at least a few miles outside the city limits. Take the train to a city and your hotel is probably only a cheap taxi ride away. You may even be able to walk. Take the plane and you travel faster and maybe cheaper, but once you've landed you have to find your way into town.