Ploidy indicates the number of copies of the basic number of chromosomes. The number of basic sets of chromosomes in an organism is called the monoploid number (x). The ploidy of cells can vary within an organism. In humans, most cells are diploid (containing one set of chromosomes from each parent), though sex cells (sperm and oocytes) are haploid. In contrast, tetraploidy (four sets of chromosomes), a type of polyploidy, is not uncommon in healthy plant species.
Euploidy, or the euploid number, is a species' normal number of chromosomes per cell. For example, the euploid number of chromosomes in a human cell is 46.
The haploid number is the number of chromosomes found in the gamete of an individual. This is distinct from the monoploid number which describes the number of unique chromosomes in a single complete set. In humans, the monoploid number (x) is equal to the haploid number (n), or mathematically x = n = 23. In some species (especially plants), the monoploid number and haploid number are not the same. Commercial rye wheat is tetraploid, with four copies of chromosomes in each cell. The gametes are haploid and contain half the genetic information of other cells, but are not monoploid as they still contain two complete sets (n = 2x).
Most fungi, and a few algae exist as monoploid organisms. Male bees, wasps and ants are also monoploid. For organisms that only ever have one set of chromosomes, the term monoploid is sometimes used interchangeably with haploid, although this is no longer the preferred terminology.
Plants and other algae switch between a haploid and a diploid or polyploid state, with one of the stages emphasized over the other. This is called alternation of generations. Most diploid organisms produce haploid sex cells that can combine to form a diploid zygote, for example animals are primarily diploid but produce haploid gametes. During meiosis, germ cell precursors have their number of chromosomes halved by randomly "choosing" one homologue, resulting in haploid germ cells (sperm and ovum).
Diploid cells have two copies (homologs) of each chromosome (both sex- and non-sex determining chromosomes), usually one from the mother and one from the father. Most somatic cells (body cells) of complex organisms are diploid. 
A haplodiploid species is one in which one of the sexes has haploid cells and the other has diploid cells. Most commonly, the male is haploid and the female is diploid. In such species, the male develops from unfertilized eggs, a process called arrhenotokous parthenogenesis or simply arrhenotoky, while the female develops from fertilized eggs: the sperm provides a second set of chromosomes when it fertilizes the egg.
Haplodiploidy is found in many species of insects from the order Hymenoptera, particularly ants, bees, and wasps. One consequence of haplodiploidy is that the relatedness of sisters to each other is higher than in diploids; this has been advanced as an explanation for the eusociality common in this order of insects as it increases the power of Kin selection. This argument has been disputed on the grounds that haplodiploidy also reduces the relatedness of brothers to sisters, theoretically balancing the above effect. In some Hymenopteran species, worker insects are also able to produce diploid (and therefore female) fertile offspring, which develop as normal queens. The second set of chromosomes comes not from sperm, but from one of the three polar bodies during anaphase II of meiosis. This process is called thelytokous parthenogenesis or simply thelytoky.
Haploidisation is the process of creating a haploid cell from a diploid cell. This is a laboratory procedure that forces a normal cell to spit out half of its chromosome content, leaving just one set. In mammals this renders this cell equal to sperm or egg.
This was one of the procedures used by Japanese researchers to produce Kaguya the fatherless mouse.
Aneuploidy occurs when a cell contains an abnormal or non-integer ploidy number. This may lead to problems in cell development. Most forms of aneuploidy in humans are lethal, but trisomy (three copies) of the sex chromosome (the cause of Klinefelter's syndrome and others) and of chromosome 21 (the cause of Down syndrome) are relatively common.
Many forms of cancer have incorrect ploidy numbers, due to the accumulation of mutations which increase chromosome missegregation.
Polyploidy is the state where all cells have multiple pairs of chromosomes beyond the basic set. These may be from the same species or from closely related species. In the latter case these are known as allopolyploids (also known as amphidiploids or allotetraploids), that are formed from the hybridisation of two separate species followed by their subsequent chromosome doubling. A good examples is the so called Brassica triangle where three different parent species have hybridized in each pair combination to form three different allopolyploid species. Polyploidy occurs commonly in plants, but rarely in animals. Even in diploid organisms many somatic cells are polyploid due to a process called endoreduplication where duplication of the genome occurs without mitosis (cell division).
Variable or indefinite ploidy
Depending on growth conditions, prokaryotes such as bacteria may have a chromosome copy number of 1 to 4, and that number is commonly fractional, counting portions of the chromosome partly replicated at a given time. This is because such organisms tend to multiply continuously.