What are the similarities and differences between mitosis and meiosis?

Similarities

Both are methods by which cells divide and replicate.

Differences

Mitosis is a one division process that produces 2 cells that each have the same number of chromosomes as the parent cell from which they were formed ie. two copies of each chromosome. The chromosomes should all be exact copies of the chromosomes in the parent cell. 

Meiosis is a 2 division process that produces 4 cells that have half the number of chromosomes  as the parent cell from which they were formed ie. one copy of each chromosome. The chromosomes will not be exact copies of the chromosomes in the parent cell because crossing over occurs to allow exchange of DNA between chromosomes. Meiosis occurs in the cells used to produce eggs and sperm. Because each egg and each sperm has just one copy of each chromosome, the cell formed at ferilisation will have copies (ie. one pair) of each chromosome.