I know there are abstract painters who say you can hang their art any way you want to--that it works in any direction. But I don't paint that way. Once I get to a certain stage in the process, I keep the same orientation and expect the painting to be hung that way.
On the other hand, occasionally a client wants a print of a square painting in a vertical or horizontal format, and sometimes it works well. Success or failure depends on the design and composition. Here's one that works fairly well in all formats:
On the other hand, some paintings simply don't work when compressed into a different format: