An "Irish bull" is a ridiculous, incongruous oxymoron that somehow seems to make sense. The name seems to come from an Old French word meaning "fraud." According to the American Heritage Dictionary, a "bull" can be "a gross blunder in logical speech or expression," and specifically, an "Irish bull" seems to make sense at first, but actually contains a ludicrous contradiction. My all-time favorite example of one is this:
When asked the difference between an Irish bull and any other kind of bull, Professor John Pentland Mahaffey of Dublin University replied, "An Irish bull is always pregnant," providing a definition that is itself an example of the form defined.
The attribution to the Irish may have grown out of the imposition of English on the Gaelic-speaking Irish and the resulting linguistic accidents, or just because English writers have historically looked down on the Irish. Some Americans famous for their Irish bulls are Yogi Berra ("No wonder nobody comes here - it's too crowded.") and Samuel Goldwyn ("Spare no expense to make everything as economical as possible"). Richard Lederer cites Sir Boyle Roche, MP (1743-1807), Member for Tralee, County Kerry, in the Irish House of Commons, as another famous source of these remarks, including "The cup of Ireland's misery has been overflowing for centuries and is not yet half full." Other examples:

I don't like spinach, and I'm glad I don't, because if I liked it I'd eat it, and I just hate it.
Clarence Darrow

If two trains shall meet on the same track, neither shall proceed until the other has passed.
Kansas state law

It seems, from what I gather, to be one of those simple cases which are so extremely difficult.
Sherlock Holmes

I don't care to belong to any social organization which would have me as a member.
Groucho Marx

"The simpler a plan appears, the trickier it can actually be."
Robin on the Batman TV show (thanks to mkb for that one.)

Sources:
http://www.word-detective.com/072302.html
http://www.gordonthomas.ie/irishbull.html
http://www.bartleby.com/61/11/I0231100.html
http://therussler.tripod.com/dtps/irish_bulls.html
http://www.ncraonline.org/jcr/0103/0103_lederer.htm
http://wordsmith.org/awad/archives/0702

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