Plasma membrane - protect cell from it's surroundings. In both kinds of cells.
Cytoplasm - supports rounded cell structure, within it are all the organelles. Contains chemicals needed by the cell. In both kinds of cells.
Nucleus - contains DNA and is the control center of the cell. In both kinds of cells.
Nuclear envelope - surrounds nucleus, makes sure important molecules (DNA) stay within the nucleus. In both cells.
Nucleolus - makes ribosomes. In both cells.
DNA - genetic information for development and function. In both cells.
Rough ER - produces proteins. In both cells.
Smooth ER - makes and stores lipids (fats). In both cells.
Golgi body - sort and process macromolecules (proteins, lipids, etc). In both cells.
Ribosomes - makes proteins. In both cells.
Vacuoles - very large in plants, a storage center. In both cells.
Lysosome - digests and removes wastes. In both cells.
Mitochondria - energy powerhouse, produce ATP energy. In both cells.
Cytoskeleton - shapes, supports, and facilitates movement. In both cells.
Centrioles - cell division (form spindle fibers). Only in animal cells.
Cilia - movement for microorganisms. Only in animal cells.
Chloroplasts - photosynthesis, helps absorb sunlight and make food for the plant. Only in plant cells.
Cell wall - strength, structure, filters molecules going in and out of the cell. Only in plant cells.
Central Vacuole - holds materials and wastes, helps maintain proper pressure within the cell. Only in plant cells.
Hope this helps!