The Bermuda Triangle is generally defined as the area between Bermuda, Puerto Rico and Miami. There is an interesting service today called Flight Aware. You can access a map of all flights anywhere in the world at any given time.
Below is a picture of the map with the Bermuda Triangle drawn on it in red. At this moment there appear to be about 20 commercial flights in the triangle. There are many flights that cross the triangle every day. So, yes planes can and do fly in the triangle.
