Sorry that I'm writing long posts, but it's actually a complex topic.
Sadly, the only "international" LEO crew transportation option is Russian, and not because the other Space Agencies and commercial entities didn't have enough time to develop one. They didn't have the resources and know-how, and rather preferred letting NASA (and Russia) to conquer these frontiers for them.
Well, European scientists and engineers didn't have less know-how than American and Russian scientists and engineers at all. Quite the opposite if we go back in history.
Actually it started during World War two in Germany, with Wernher von Braun and his team in Peenemunde (the most modern rocket research institute in the world back then, and the first place to launch a vehicle into space). Not really something to be proud of, because von Braun actually was a war criminal, but on the other hand still a phantastic visionary and engineer, who significantly influenced the US space program not only by designing the Saturn V (he also became the director of the Marshal Space Flight Center). He talked about space stations that are being supported by "Space Shuttles", long before NASA orbited the Moon manned for the first time in 1968.
Of course European engineers did not get the resources and budget to compete with Russia and the USA in space in the 1960s, simply because they did not get such an assignement politically. But the know-how was there, on the same level. The Concorde was developed in the 1960s by French and British engineers as one example. It was the first civil aircraft that used fly-by-wire (and also thrust-by-wire), and most importantly: that could fly with Mach 2 for more than two hours without using reheat. This was and still is something no other airplane can do, while also carrying 100 passengers. Concorde was even more successful than its only, Russian competitor, the "Concordski" (Tupolev Tu-144). Another example is Airbus, which is more than just a serious competition to Boeing. Airbus meanwhile sells more aircraft per year than Boeing. A few American airlines even completely change their fleet by Airbus aircraft, because it is the most modern commercial jet aircraft (now the A380, which is without competition). The US government even was looking for the A380 for their Air Force One, but Airbus denied because of understandable reasons (selling their technology to the US government might not be the best idea in terms of competition to Boeing...).
If we talk about ESA: with the tiny budget ESA gets, ESA is amazingly productive, not only because of the Ariane launchers (just look at the research fields and contributions to manned and unmanned space flight technologies, not only "Columbus"...). ESA engineers do not have any less know how than Russian and American engineers. They just don't get the budget and assignment to develope a manned system. It's a political issue, not a know-how issue.
In future Europe will operate both, the Ariane and Soyuz at Kourou, and possibly also the smaller Vega rocket. The ATV, which already services the ISS, is planned to be changed into a manned system.
If we look how Europe and meanwhile Russia and the USA manage space flight and aviation industries, I think that desktopsimmer is rather right: co-operation is the future. Also for NASA, because its current program structure is not promising at all. I doubt they will get the chance to operate a new manned system within this decade. But just like for Europe: the reason is not a know-how issue, but a political and budget issue. In fact, the most amazing outcome of NASA research and development took and takes place in the unmanned space flight and earth sciences, not in the manned space flight. something a lot of people don't think about or don't even know. The manned part of NASA is just the part that gets the most attention. But there is way more that NASA does, beside launching manned rockets in Florida. This is something the USA still can be really proud of, in terms of a national space program. Loosing Constellation is not so hard as it seems to be to some people. Constellation was canceled just early enough, before it turned into a real disaster...