I am planning a 3 week backpacking trip going from London, Paris, Amsterdam, The Alps, Venice, Florence, and finishing in Rome. How easy is of it to travel by train? Are high speed rail an extra cost if you have a rail pass?
Train travel in Europe is certainly easier than the US. But you'll need to keep moving if you want to hit 7 destinations in 21 days. Can it be done? Yes, but you will spend a lot of time on the train. One of the biggest mistakes people make is underestimating the time it takes to get from place to place. You're looking at 3 days in each location. Don't count your arrival day (you'll be too tired) or your departure day. You could probably allot 2 days each to Florence and Venice, but it's still an ambitious trip. I assume you are young and energetic and that will certainly help. You might want to check out www.bahn.de which will show you the trains available and how long it takes to get where you want to go. A six hour train ride plus time to check in to your hotel and get situated will consume most of your day. And yes, the dirty little secret of rail passes is that you will pay a supplement for high speed trains and many of them will need to be reserved in advance. In some cases, all you get from the pass is a discount on a premium train ticket. I don't usually push the blue books, but in this case you should definitely read Europe Through The Back Door if you have not already done so.
Go to www.seat61.com for all the train tips you are likely to need. Likewise the other poster, you are likely to see more of the inside of a train car than any of the destinations you have on your ambitious list. You can do Amsterdam on one overnight from Paris and then move on, skipping the Alps unless you want to see the French Alps on your way to Venice. Be sure and stay flexible in case you fall in love somewhere along the way.....