Yes, there are several examples of two-dimensional objects and organisms. However, it's important to note that true two-dimensional entities do not exist in our three-dimensional physical reality. The examples I will provide are representations or approximations of two-dimensional concepts.
Flatland: "Flatland: A Romance of Many Dimensions" is a satirical novella written by Edwin A. Abbott in 1884. It explores the concept of a two-dimensional world inhabited by geometric shapes. While this is a fictional work, it provides an imaginative representation of life in a two-dimensional space.
Computer graphics: In computer graphics, two-dimensional objects are extensively used and can be seen on screens or printed materials. These objects are represented using coordinates on a plane and typically include shapes, images, and text.
Single-layered organisms: There are organisms that appear to be two-dimensional due to their physical characteristics. For example, some types of algae, such as diatoms, have flat and thin structures. Similarly, certain microscopic organisms like flatworms (Platyhelminthes) have flattened bodies.
It's worth mentioning that even though these examples may appear two-dimensional, they still possess some thickness or depth in reality. True two-dimensionality, where an object or organism has no thickness whatsoever, is purely theoretical and not achievable in our physical world.