During meiosis, chromosomes can be distributed unevenly to the daughter cells--this is nondisjunction. If two sister chromatids stick together instead of separating, one daughter cell with have an extra copy of the chromosome, and the other will be missing a copy. As a result, if an offspring forms from these cells, it will have either three copies of the chromosome or only one. Another possibility is that all of the sister chromatids fail to separate, resulting in a cell with two sets of chromosomes--this is known as polyploidy.
Many such chromosomal mistakes are so severe that they are incompatible with life--any embryo will be spontaneously aborted long before birth. However, there are some that can be carried to term, such as trisomy of chromosome 21 (have three copies of it)--commonly known as Down syndrome. Other examples include polyploidy of sex chromosomes, resulting in Turner Syndrome (an XO female), Klinefelter's Syndrome (an XXY male), XYY Syndrome, and others. Most of these don't have many noticeable effects, and people with them may live their lives without finding out for a considerable time, although anyone that does certainly will be infertile.