What is International Bitterness Unit (IBU) for beer?

The International Bittering Units scale, or simply IBU scale, provides a measure of the bitterness of beer, which is provided by the hops used during brewing.

The bittering effect is less noticeable in beers with a high quantity of malt. The technical limit for IBU's is around 100.

A light American lager might be as low as 5 on the scale, while barley wines, India pale ales, or imperial stouts can range up to 100 or higher.

A light American lager such as Budweise might be as low as 5 on the IBU scale.

An Irish stout can have IBU as high as 60.

IBU measures for other beverages include:
Belgian Lambics: 11–23
Blonde ale: 15–30
Märzen/Oktoberfest: 18–25
Ordinary English bitter: 20–35
Porter: 20–40
Brown ale: 15–25, with North American styles higher, 25–45
Bohemian-style Pilsener: 30–45, sometimes it can range up to 100 (e.g. German Bitterpils)
India pale ale: 40 or higher
An Irish stout: 25–60 (eg. Guinness ~45 IBU)

References:
International Bitterness Units scale. Wikipedia.

The sad state of German beer culture - Slate Magazine, 2011.
Oktoberfest: 5 delicious styles of German beer - Slate Magazine, 2011.

Related:

The Economist explains: How IPA beer conquered the world http://buff.ly/1k1DUaR