That's true, there is no radar coverage over the atlantic ocean, at least part of it. But I wouldn't say that the planes are on their own.
You have different types of air traffic control: the most common is radar control like in North America, Europe, most Asia... But in some other parts of the world, there is no way to get such ATC, for different reasons. Over the Atlantic ocean for instance, you would have to put several radars on ships, which is not feasible. Elsewhere like the African continent, it's mainly because of a lack of finance.
Although you have no radar coverage, it doesn't mean there is no ATC service provided. HF Radio transmission is always connecting the pilots with an ATC centre. The main difference is that the distance separating 2 aircraft flying on the same airway at the same level is huge and speed is restricted.
The Atlantic is the most famous example of what we call "procedural control". But I can give you another unsuspected one: Have you ever flown let's say from Europe to Asia, routing through the Arabian peninsula, crossing the Indian ocean towards India?
The last Arab country you will be overflying is Oman providing radar control up to the western third of the Indian ocean. Then it is procedural control as soon as you enter Mumbay (Bombay) FIR until about 200 nautical miles (Nm) west of Mumbay.
Therefore, Oman ATC has to provide a 10-minute separation between traffic flying same route, same level. Can you imagine what is a 10-minute separation: 86 Nm! This is huge! In some other countries, this separation can be extended to 15 or 20 minutes compared to the 5 or 8 Nm separation used under radar control! (en-route)
In conclusion, I'd say that you should not feel unsafe just because there is no radar covering the pond. No radar doesn't mean no ATC!
The sky has no limit...