Aneuploidy is a condition in which an individual - known as an aneuploid - or cell has a variant number of chromosomes but the variation does not involve an entire chromosome set. These latter cases fall into the category of Polyploidy.

Aneuploidy commonly involves one chromosome too many or too few but any aberrant number less than an entire set (n) is possible. The cause of aneuploidy is nondisjunction, which is a failure in chromosome segregation during cell division. (In the case of aneuploidy it is failure in only one or a few chromosomes if all chromosomes fail to segregate then the result will be polyploidy.) Resulting gametes carry either no copy of the chromosome that underwent nondisjunction, or an extra copy. The general terms used are:

Nullisomy: The lack of any copy of a particular chromosome.
Monosomy: Having a single copy of a chromosome (in a diploid organism).
Trisomy: Having an extra copy of a particular chromosome.

In humans, there are no viable nullisomics for autosomes and there are only three autosomes for which live birth trisomies are observed. These are:

Trisomy 13 Patau Syndrome
Trisomy 18 Edwards Syndrome
Trisomy 21 Down Syndrome

For the X and Y chromosomes, aneuploids are:

X Turner Syndrome
XYY Sometimes called XYY Syndrome but there are no specific phenotypic effects.
XXY Klinefelter Syndrome

Karyotypes:

45 X Turner Syndrome
47 XX +21 Down Syndrome
48 XY +7 +12

The Nature Scitable page on aneuploiy.

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