It is often heard that vegetarian movements are on the rise recently. Is there any place or country in the world, where the vegetarians are in the majority at present?
Assuming you mean >50% of the population in an area by majority, the answer is no, there are no countries where this is true.
According to Wikipedia, the country with the highest amount of vegetarians is India, with a (rather staggering) 29%–40% of vegetarians. That's approximately 361 million people, which is hard to visualise, I'd say.
This article claims that the Rajasthan state of India is the 'most vegetarian', with approximately 75% of the population being counted as vegetarian. However, being a state of India and not a country, it doesn't change the fact that no whole countries are majority-vegetarian.
If you're interested in the other side—areas with the least vegetarians—Wikipedia states that only between 0.5%–4% of Spaniards are vegetarian. That's about 1.8 million people in Spain who are vegetarian, according to the estimates used by Wikipedia.