Derailed Train of Thought

No doubt the train of thought of every passenger aboard that train was derailed.

Ptraci didn't just derail the train of thought, she ripped up the rails, burned the stations and melted the bridges for scrap.

—Terry Pratchett, Pyramids

This is what happens when you try to have a conversation with a Cloudcuckoolander. You try to talk to them about the weather, and then they get started on pink unicorns and that website with all those strange literary devices. In essence, the Wiki Talk is when one character becomes so sidetracked by one train of thought that he completely forgets about the original topic.

Characters prone to this include the Cloudcuckoolander (as mentioned above) and The Ditz. The Only Sane Man (who is often subject to this) can respond with a facepalm, some form of internal monologue expressing his disbelief, or an attempt to remind the invoker of this trope what they were talking about in the first place. Occasionally, the subject material brought up in the Derailed Train of Thought can result in the recipient receiving Too Much Information. Responses may include the Spit Take, and for added humor, the invoker of the Derailed Train of Thought may remain unaware of the reaction he/she has caused.

Sometimes, the invoker of this trope may not be a Cloudcuckoolander, but is extremely embarrassed and, as such, wants to turn the subject to something different. Or it could be a Cloudcuckoolander who also happens to be extremely embarrassed.

Compare also with Non Sequitur, in which it is heavily implied that the character should be discussing one thing, but one of them goes completely against those expectations. In this trope, it is made clear by an initial statement what the conversation is about, and then one character turns the topic to something completely different. Observe:

In Non Sequitur (taken from their page):

What we need is some way to stay in contact over long distances. Some sort of communication or "telephonic" device which is "mobile"... Of course! That's it! We'll train messenger pigeons!

In Derailed Train of Thought:

Alice: We'll need something to stay in contact over long distances. I think a cell phone should work, how about you?
Bob: That would work. Say, have you ever thought about how a cell phone and a cell could be related? Maybe the cells in our body have little cell phones implanted in their DNA. Speaking about DNA, have you...

Notice that in the second example, Alice specifically stated that they were going to talk about cell phones, whereas in the first, it was merely implied.

Related to Wiki Walk and Seinfeldian Conversation, in which the conversation is pointless but not necessarily unrelated.

Examples of Derailed Train of Thought include:

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Anime and Manga

Azumanga Daioh: Osaka, Cloudcuckoolander extraordinaire, does this at least once, with a discussion on japanese characters that starts with hemorrhoids and goes on to the proper way to write kanji, and then to sea life.
In the Bleach anime, Orihime manages to produce the epic Leekspin meme in an Epic Tangent resulting from a crash-in with Ichigo in their school hallway. He asks if she's okay, this results from her embarrassment of bumping into him.
In Fullmetal Alchemist, Ed would rather recite the periodic table than talk about his potential love for Winry.
Everyone who tries to talk to Isaac and Miria. Everyone.

Film

Played with in the fourth Lethal Weapon movie, where Chris Rock and Joe Pesci go off on a huge tangent about cell phones, for no apparent reason.
Happens briefly to Lightning McQueen at the beginning of Cars when pysching himself up for the race.

Lightning: I eat losers for breakfast... Should I have had breakfast?

Literature

Luna Lovegood of Harry Potter often manages to turn a conversation into something about the magical equivalent of Bigfoot and the Loch Ness Monster. Many of the conversations she starts begins with her saying something completely ordinary, and then turning it into this trope.
Neal Stephenson's Anathem seems to do this several times, but every single one of them turns out to be a Chekhov's Gun of some sort.
The narrator of Mark Twain's "The Celebrated Jumping Frog of Calaveras County" asks an old man about someone named Leonidas W. Smiley. The old man says he has never heard of anyone named Leonidas W. Smiley, but he has heard of someone named Jim Smiley. The rest of the story comprises a Rambling Old Man Monologue about Jim Smiley and his jumping frog.

Live-Action TV

In Seinfeld, George's boss, Mr. Steinbrener, always gets sidetracked by one thing or another when George tries to talk to him.
The Tenth Doctor, on Doctor Who.

This is my timey-wimey detector. It goes ding when there's stuff. Also, it can boil an egg at thirty paces... whether you want it to or not, actually, so I've learned to stay away from hens. It's not pretty when they blow.

The Swedish comedy show Hipp Hipp had Melodikrysset, a musical crossword aired on radio, wherein the host would play a song and then explain whet you were supposed to write. After playing In the summertime the explanation is as follows.

The Host:That was In the summertime by Mumbo Jerry and it's about the summer, in the summer people like having ice-cream. Personally I'm fond of 88:an. 88:an has crushed nuts in it so therefore Pungspark goes on vertical no. 13.

Newspaper Comics

In Calvin and Hobbes, Calvin often goes off into these. Watterson, apparently, based Calvin's tangents off of his own wife.

Western Animation

Many of Seth MacFarlane's works are prone to this. Family Guy and The Cleveland Show employ 10-second shorts to provide comedy, connected only to the dialogue by a "Just Like X" statement made by one of the characters.
Invader Zim- Don't even try to have a coherent conversation with Gir

Real Life

English teachers who actually don't hate their job seem to be rather fond of doing this.
The news sometimes segues into new stories using incredibly strange logic.