Eukaryotic species can be unicellular or multicellular—the defining feature of a eukaryotic cell is that it has a nucleus. This sets it apart from prokaryotic cells (and therefore from the domains Bacteria and Archaea), which tend to be less complex and less compartmentalized. There is no set number of cells that an organism must have to be considered a eukaryote.
Examples of unicellular eukaryotes include yeast, algae, dinoflagellates, and some types of fungi. Multicellular eukaryotes include just about any plants and animals you can think of. In general, more complex organisms not only have more cells, but they have more types of cells.
For example, the human body has an estimated 30–37 trillion cells. However, within the body, these cells serve different purposes, and there are at least 50 types of cells that make up a person. The human brain has approximately 100 billion neural cells. Humans also have about 1.6 trillion skin cells (or epithelial cells) and 15,500 hair cells (these cells are found in the inner and outer ear and are responsible for transmitting vibrations to the auditory nerve, where they are translated into sound).
Eukaryotic organisms are incredibly diverse and incredibly complex when it comes to cells and cellular interactions across different systems.