ManoDantukai.lt was founded by me (Ričard Chmyznikov) while I still was a dental student in my home country, Lithuania. I found that this type of website was - and is - of great demand accidentally, when I created a Facebook group called "Lithuanian Dental Students Forum", which quickly gathered a lot of dental students to it(currently there are over 1300 members - dentistry students and latest graduates). In the group students began to sell equipment and materials to each other and most importantly they started sharing patients for their practices. Some students would write "Looking for a patient with such and such problems for such and such day" , others would simply give away contacts of patients that they had found but couldn't take themselves.
This is how I understood that something serious was going on there, as the amount of such posts was overwhelming. It was obvious that students were having hard time finding patients, so I decided to create and promote a website where a lot of people from my country could register in order to get free dental services by dental students. We needed as many patients' registration forms as we could get, in order to find the perfect patients to practice on. This is why I wrote to several online newspapers and offered them to inform people about such a possibility (and, obviously, to advertise for free) and one of them replied positively. After the interview was published it was the most read article on 15min.lt for two days. After the article, most popular TVs contacted me and took interviews from me and made reports about this problem that ordinary people and students encounter and told about my website.
That's when the fun began. We got hundreds, then thousands of people registering on my website. In a few days from mere 250 registrations we jumped to over 2 thousand. So, the students were happy and patients were happy for getting free dental services and left great feedback on the website.
However, I wasn't very happy, because not all patients were taken by students. In fact currently out of 5000 patients registered only a bit over 1000 were taken by students. So I thought I had to do something with the rest 4000 patients. This is when I understood it could be made into a business. I felt that many of those patients, still having their teeth hurt, would go to an ordinary dentist anyway even though they would have to pay for it.

Currently me and a friend of mine (a programmer) are developing a platform, that would enable:

1) Patients to register for free dental services.
2) Dental students to market themselves and get patients to practice on.
3) Dentists to market themselves, fill empty schedules and increase income.

What's more, I believe this type of platform would be applicable for other specialties as well all over the world, thus making it a hugely scalable business.