Spain has the second biggest high speed train network of the world, with over 3.000 km (many more kilometers being built), just after China.
This 2014, 28M people will have traveled by train, compared to 31.2M in USA in 2012. The goal is to reach 56M in a few years. After many years where the prices were expensive, we have started to liberalize it and prices have go down. Now it's reasonable cheap. You can buy one-way tickets for 30€ for a 1h30 route (like 4h by car). Madrid-Barcelona is one of the most demanding routes and flights can't compete with the high speed train. In just a few years, people have moved from using flights to most of them using the train. It's way way more comfortable.
Of course, the key question is geography. Trains works best for a distance less than 1.000km. In Spain that's the distance from east to west or south to north. In USA there are some areas that make a lot of sense like Boston-NY-Philly-Washington; and California.
In the UK, we tend to look enviously at our continental neighbours such as Spain, France, Germany, Netherlands who we pereceive to have fast, modern, reliable and cheap rail travel. All things that we tend not to have in the UK (especially the cheap bit).
One interesting fact I discovered a while ago that greatly surprised me: the percentage of public transport usage (as the main mode of travel) is higher in the UK than in Germany, France and the Netherlands. This finding came from a survey funded by the European Commission in 2010/2011.
Country and % whose main mode of travel is public transport
Czech Republic 37%
Spain 30%
UK 22%
France 20%
Germany 15%
Ireland 14%
Finland 13%
Denmark 12%
Netherlands 11%
The UK has a higher share for public transport than the Netherlands in large part because the Netherlands has a higher share of people who use no mechanized transport at all: 34% of Dutch either bike or walk as their main mode of travel, compared to about half as large a proportion of Britons (16%), according to the source you linked.
Here's the ordering (same countries, same source) if you take transit+walking+biking together:
Czech Republic 60%
Spain 46%
Netherlands 45%
UK 37%
Denmark 35%
Germany 35%
Finland 35%
France 32%
Ireland 30%
The UK still does pretty well, admittedly. I think the reputation for bad trains in the UK is mostly intercity trains, whereas these "main mode of travel" statistics are more about commuting, which is a different set of concerns; the London Underground alone accounts for a very large number of commuters.
(Denmark, by contrast, doesn't look anywhere near as good as its reputation in these kinds of figures. In large part because its reputation is built specifically on Copenhagen, the most visible city by a good margin. Jutland, which has about half of the Danish population, is a sprawling, car-centric collection of towns and suburbs.)
I really don't think the Spanish AVE is something to be proud of. The only purpose of building most of the lines was political. And well, because with big projects many politicians can get rich.
The total cost of the AVE has been estimated in over 50 trillion euro, and in some lines they don't even get 100 passengers a day.
Probably, public transportation doesn't need to be build taking only into account the short-term economic profit, but in Spain they just burnt a massive amount of taxpayers' money in a useless infrastructure. And Spaniards will struggle for decades to pay the dept... if they manage to pay it at all.
Spain has the second biggest high speed train network of the world, with over 3.000 km (many more kilometers being built), just after China.
This 2014, 28M people will have traveled by train, compared to 31.2M in USA in 2012. The goal is to reach 56M in a few years. After many years where the prices were expensive, we have started to liberalize it and prices have go down. Now it's reasonable cheap. You can buy one-way tickets for 30€ for a 1h30 route (like 4h by car). Madrid-Barcelona is one of the most demanding routes and flights can't compete with the high speed train. In just a few years, people have moved from using flights to most of them using the train. It's way way more comfortable.
Of course, the key question is geography. Trains works best for a distance less than 1.000km. In Spain that's the distance from east to west or south to north. In USA there are some areas that make a lot of sense like Boston-NY-Philly-Washington; and California.