There are many reasons for that. The main reason for those who come from former Soviet countries is the simple habit, because they were grown up on this seaside. Almost each working person in the past Soviet Union could get in summer a trip to Black Sea rest-places half-paid or completely paid by the government. Another reason is that this sea is the most southern located from all the seas that are bordering direct the former Soviet Union countries and is of course most accessible.
There are 5 countries that have claimed a piece of coastline at Black Sea. These are Turkey, Georgia, Russia, Ukraine, Romania and Bulgaria.
The Turkish part of the coastline is the longest one and is generally preferred by European travelers mostly because of the good marketing campaigns of the travel agencies and is actually, the cheapest possibility. In the last time the prices are quite high there and the quality of service should be double checked and the place of stay should be selected with great carefulness. Though, for a little higher amount of money, one can get quite a good service there. The most frequent visitors are travelers from Germany.
The Georgian coastline is very special with its rocky parts. Imagine the huge rocks coming out of the sea, a short, about 20 meters rocky beach and mountains beginning right after the beach. You could find a cave there, make a camp, place some tents and spend a week or two diving, climbing on the mountains, hunting fish and crabs, gathering starfishes. The sea water is perfectly clear here even if it is 25-30 centigrade warm. Such a week would be an unforgettable one and I would really spend some more weeks there.
The Russian coastline is rich with pensions and holiday homes built in soviet time for the collaborates of the Soviet Party. Some of them are already ruined with the time, and some of the were sold to private persons and companies and are held in quite a good state to have a rest in them.
The Ukrainian part has two different types of places. The first of them is the usual coastline of Odessa region and the neighboring, which is characterized with high temperatures, burning sun, sandy beaches and quite inexpensive possibilities for a traveler. The second one is Crimea semi island, which is characterized by separate climatic conditions and even separate flora and fauna. There you can find rocky beaches along with the sandy ones, lots of pensions left from soviet time, which are held in a very good state. It was actually one of the most beloved and privilege seasides of the Soviet Union and till now it is quite a good one to travel to.
The Bulgarian and Romanian parts of the coast are targeted mostly on the European market and in the last times the prices are much higher than quality, at lest in Bulgaria, but if not to consider the prices, Bulgarian coastline is quite well equipped and served and the time spent there won’t be appreciated as lost, so it’s worth traveling.