Shape is the decision people skip past to get to colour, and it's usually the one that matters more. A rectangular rug follows the lines of a room — walls, sofas, dining tables — which is why it's the default and why it almost always looks correct. A round rug breaks that logic deliberately, and it only works when something in the room is asking for it.
The clearest case for round is a round table: a circular dining table or a round coffee table sits naturally on a circular rug, echoing its own shape rather than fighting a rectangle underneath it. It's also useful in a squarish room with no obvious axis to follow, where a rectangle can end up looking arbitrary and a circle reads as an intentional anchor instead.
Free-form and shaped rugs — pieces like Solstice Arc or Canyon Agate — sit in between. They're not trying to match the room's geometry at all; they're meant to be looked at as objects in their own right, which works best in a space with enough open floor around them to actually see the silhouette. Boxed in against furniture on every side, a free-form shape just reads as an odd rectangle.
If you're not sure, default to rectangular. It's the safer choice precisely because it's the expected one, and a rug's shape should earn its departure from that default rather than assume it. Round and free-form pieces reward a specific setup; a straightforward rectangle works in almost any room you put it in.