Train travel is extremely convenient and well-designed. Look out for tourist information booths located in city train stations. Trains are usually filled with local people as well, and can be a great place to meet interesting locals. Do not be surprised to see pets on many trains. Most trains have separate smoking and non-smoking cars, and larger trains have a buffet car and person that comes down the aisle with a pushcart of snacks and drinks.
Train tickets range from very inexpensive to very expensive.
Generally, tickets in the northern parts, such as Scandinavia, cost tremendously more than tickets in the southern parts, such as Italy. For most people that want to see a lot of area, especially if not exactly committed to a route, some sort of rail travel pass is a good idea. Just ask the travel agents at your home for the passes, but be sure to purchase them a few weeks before you leave, since they take a bit of time to arrive. Although this section is getting lengthy, I want to mention overnight trains. I took two of these, and had one bad experience and one good.