I wonder are there places in the US where "marshroute taxis" (not sure about the correct name here) are available? Basicly these are small vans/shuttles (10-12 seats), going by a fixed route, which you can stop and get off at will.

In many European countries they are very popular, being much faster and regular than buses; and much more affordable than regular taxis or a personal car. I suppose they will also be a good idea for small-scale personal business in the future to come.

While this ("marshroute taxis") is a good idea, a similar grass-roots business whereby locals were running shuttle services for hikers has been pretty effectively killed by legislation requiring special licensing, insurance, etc. maing it cost prohibitive to operate such a business. This is especially true, since for most of these folks,it was just a way of earning a few extra dollars on weekends.
If you are in a situation where everyone knows and trusts each other, fine.  Otherwise, the passengers are no safer than hitchhikers.
This is a question of balance. You can provide licensing and insurance framework that can ensure the safety needed, without killing the business before it even started.

In this regard I find the legislation environment in the US quite discouraging for the small businesses. Only a large company could afford to pay for those licensing fees or to potentially meet the prodigious liability claims that are common here.

Our current climate would have killed many existing ventures had it been in place back when they started.

Can you imagine getting approval for heavier-than-air passenger travel?  Basically the only reason it exists is because they can point to a long (relative) safety record, which they have because of the many sacrifices of the pioneers who took huge risks to test new designs.  

If you were trying to start the "Air travel industry" from scratch now, not only would the NIMBY's prevent any airports at all from being built, but every govt from local to national would have to be convinced that the things wouldn't plummet out of the sky or cause unforeseen environmental damage or what have you.  It would take decades before anyone permitted even a pilot project (ooh, bad pun, sorry) to get off the ground (groan).

This is very educative for countries, making their first steps in the market economy like the countries in Eastern Europe. With the European integration and the modernization of their economies it is often the case that Western standards are being applied in a pretty straightforward manner. It is ideologically forgotten that the viability and applicability of these standarts are a result of many years of accumulation of capital and infrastructure and evolution of traditions, buseness relations, legislations etc. The idea that these standarts will be reached by simply enforcing them by the government is simply silly and very counterproductive.
LevinK makes a good point: these vans driving regular routes make a nice compromise between buses and cars. Just to toss out a few numbers - in Vilnius (capital of Lithuania), a municipal bus fare is roughly 40 U.S. cents. To get where you're going, that bus might take anywhere from 20 to 45 minutes. In contrast, one of these vans driving the same route as that bus will charge from 70 U.S. cents to $1.40, but will get you to where you're going in half the time or less.

I'm not sure how the vehicles compare in terms of mileage per gallon (or, as they say around here, in liters per 100 kilometers). The bus fleet and the van fleet are in an arms race, with the municipal guys and the private guys buying newer and newer vehicles. Don't know who's ahead, at the moment. Maybe the vans.

I guess more important would be what is the fuel consumption per passenger kilometer. These vans usually have not very big diesel engines - making probably around 17 mpg. With 7 passengers on average the overall efficiency would be better than a 2 passenger 55 mpg Toyota Prius (119 vs 110 passenger miles/gallon).
On the South Side of Chicago they are called jitney cabs. They are very illegal, serve as many people as does the regular city bus system(though mostly a.m. & p.m. rush). The city needs them & tolerates them. Same system on smaller scale throughout Black America.
During the 1980s there was a safety problem of mostly truckers on drugs causing accidents as well as things like school buses being driven by students. Truckers were carrying licenses from several states to avoid too many penalty points from being accumulated on any single license. So the Feds created the Commercial Driver's License system. They also imposed mandatory drug testing that is so expensive it costs nearly $100,000 per violator caught. A person now must prove they know the rules of the vehicle they are operating as well as the skill to do the job. They must pass the drug test which has discouraged users from entering the profession. They must pass a medical exam every two years. The only fixed requirement in passing the medical is a blood pressure under 140/90. Beyond that its the judgement of the doctor. I am not aware of any scientific study that has shown that the CDL laws and drug testing has improved safety. As long as a company doesn't cross state lines drivers can and are pushed to work overtime so much that fatigue is a serious safety problem.
A similar system exists in SE Asian countries. In Thailand it is very common to see both bok-bok and sangthaew that carry from 7-20 people in something equivalent or similar to a converted pickup. In fact they are now running with prices less than the local city bus system and causing some anguish as some bus companies in Bangkok are now holding protests about inability to compete with these little guys.

In most western countries people would not even consider these types of things due to safety concerns whereas here it quite expected that you would stand off the back hanging on for your life. I suspect that as the prices rise and the world changes we will see much more of this kind of thing long before we see people simply deciding not to go anywhere. So even if people cannot afford to drive to work in their SUV the day will come when they may be forced into using some form of shared transport to get to work.

Of course, that will only happen once other measures like invading and stealing the oil have been exhausted but I don't think those plans are likely to be successful for too long anyway.