There were at least two presidents (Harrison and Garfield) who did not deliver a State of the Union address. Their terms were both less than a year long and ended with the death of the president, so it seems probable that would be the reason (though it would require further research to determine).

The custom of the speech was established by Washington, but Jefferson abolished it when he became president as he thought it too "monarchical" a behaviour. Instead he had it delivered as a written letter to congress. This was how it was done until Wilson who in 1913 instead delivered it as a speech, thus re-establishing the custom. Even then there have been many presidents since that who has instead opted for the letter (Wilson himself did this in his last two years as president, citing health reason). The last president to choose that option was Carter in 1981.

Furthermore the date of the address has changed through time, as the constitution was amended in 1934 so that congress opened in January rather than March, leading to a corresponding change in the time of the address.

Additionally the term State of the Union was first used in 1934 and it has not been consistently applied since then either. Reagan in 1981 called his the "Address Before a Joint Session of the Congress on the Program for Economic Recovery" for example. The purpose and concept has been around since Washington however, naming aside.

I realise this does not answer your question very well, but it is at least background.

Here's a source for the above claims and further reading material.

EDIT: Now, if I may pose a question myself does anyone know if the CSA president also delivered a "State of the Confederacy" address while it was around?

Related question. Has a President ever listed the State of the Union as anything other than strong?

I do not know of one that went horribly wrong, but I can tell of one that had horrible consequences for that President. Grover Cleveland in 1887 proposed in his State of the Union address (then sent to Congress in written form instead of delivered by the President) to reduce tariffs. Republicans and protectionist Democrats thought lowering tariffs would be bad for American industry. That became the prominent issue in the 1888 election and lead to him losing.

http://www.presidency.ucsb.edu/ws/?pid=29528

http://millercenter.org/president/cleveland/essays/biography/3

http://www.historycentral.com/elections/1888.html

I just finished reading Theodore Rex which does talk about the themes and reception to all of his annual written messages, and while none of those went horribly wrong, I am reminded of another episode related to an annual event -- the Gridiron Club Dinner. While I realize that this is not exactly related to the OP's question (and the president does not always attend), I think it is something that is noteworthy in just how badly it went. After viewing a caricature of Senator Joseph Foraker relating to the absolutely horrible way TR handled the Brownsville affair, President Roosevelt interrupted dinner service to speak and launched into basically an angry tirade about it. Theodore Rex goes on to mention that by tradition, nobody spoke after the president, but given the situation, Senator Foraker was allowed to speak and to try and rebut the president, during which, TR tried to interrupt again (but was stopped by Blythe, twice). At the end of Foraker's remarks, TR got back into it.

That incident came to mind, but otherwise, the only other thing I can think of happened in the last twenty years (and so we cannot really discuss it here because of the rules about that) and was very, very minor in the grand scheme of things.