Y-DNA testing, the analysis of markers in the male chromosome, was the first to be offered to the general public, in 2000. Over the past dozen years increased depth of testing has become normal.
Naturally, since it is analysis of the male chromosome, it is not a test that can be performed directly for women. However, if they have a brother or father willing to help, that information is definitely useful in a genealogy context.
The best testing, since it agrees with the technique having the greatest database for comparison is Y-STR testing, which is offered by FamilytreeDNA.
Many surname and geographical projects have been set up, and with a 37 or 67 marker kit, it is a valuable contribution to finding common ancestors.
23andMe tests Y-DNA also, but as part of its SNP process. Although the STR and SNP processes cannot be directly compared, the SNP analysis can infer a level of analysis approximately the same as the 37 and 67 Y-STR marker testing of ftdna.
The higher levels of testing can also be effective in determining the relationship of two men.
Haplogroups are the similar groupings of Y-STR samples, and the way they are related to each other, and knowing which changes came first, tells the story of migration, gives a rough gauge of timeline, and of the individuals who are related to each other.
Within a particular haplogroups there are secondary groups, called sub-clades.
Some of the Y-DNA haplogroups are very common indeed, an example being the R1b in the British Isles.
For an excellent overview of Europe's Y-DNA haplogroups, Eupedia has excellent coverage. There is also coverage by Region and by Country.
For a worldwide view of Haplogroups, start with this page. Fascinating views, and if you scroll to the bottom of the page, links to secondary pages that include native American haplogroups.
One Name Studies
One way to contribute to wider knowledge is to test your Y-DNA as part of a surname study. FamilytreeDNA has hundreds of such projects, with the list found here.
An excellent article by Pomeroy providing a well thought plan for analysis of a surname is linked here as a pdf.
Haplogroups of the British Isles
The chart below is based on the sample numbers available through the Eupedia Country and Region databases.
Note in the above chart how R1b dominates the Y-DNA landscape in the British Isles. I1 that includes both Vikings and Angles, is next in importance, but far below the R1b haplogroup. In Eastern Europe Haplogroup R1a dominates almost as much, but throughout Europe other groups have pockets where they reach some considerable levels. Scroll down through the page at Eupedia.
Y-DNA Haplogroups in 1500
The Y-DNA Haplogroup map is based on the best archeological, anthropological and modern information. The Y-DNA map of today by comparison has greater admixture of European Haplogroups in North America, for example.