What are the differences between plant and animal cells?

Plant cells have a cell wall, as well as a cell membrane. In plants, the cell wall surrounds the cell membrane. This gives the plant cell its unique rectangular shape. Animal cells simply have a cell membrane, but no cell wall.

I would like to add to Tara Stirland's answer: both plant and animal cells have a cell surface membrane as well.

Both plant and animal cells are eukaryotic cells and so both have a nucleus, mitochondria, ribosomes and cytoplasm. In addition, plant cells have a vacuole, chloroplasts and a cell wall.