There are about 50 repairs in the Atlantic each year. The cables are damaged by anchors and fishing lines and even things like shark bites and whale entanglements.

I remember Egypt getting cut off as quite a big story here (UK), http://dailystaregypt.com/article.aspx?ArticleID=18746

Google it, it seems to happen every few months but most countries have some limited backup.

Latest appears to be this one, http://allafrica.com/stories/201007290937.html

There is also at least one submarine out there that has probably been modified to access submarine cables:

http://en.wikipedia.org/wiki/USS_Jimmy_Carter_%28SSN-23%29

The US tapped an undersea Soviet cable in the 1970s:

http://en.wikipedia.org/wiki/Operation_Ivy_Bells