But I Digress

Everybody loves a speech, especially when it helps sort out the life or relationships of the characters you've been following for the last hour and a half. But wait... isn't this a bit inappropriate for the context of the speech? Why is Bob talking about his rocky relationship with Alice and the zany adventures they'd been through in the last week, when the audience is here for the Annual Refrigerator Salesman Awards? It doesn't matter that Bob should have been pulled offstage before the often-lengthy speech could end, everyone still bursts into Spontaneous Applause at the end (whether Alice responds favorably or not).

Common in valedictorian speeches, where the student is expected to make their own speech but tends to forget about anything that doesn't have to do with the plot of the film, College Movies where the protagonist gives a What Have We Become speech, and romantic comedies/dramas, as in the example above. Differs from Character Filibuster in that the character is supposed to be giving a speech, but what he says has little to nothing to do with the speech's official purpose.

Contrast Disorganized Outline Speech, where the speaker is on topic, but can't seem to get to the point. Compare Holding the Floor, where the speaker is digressing deliberately to buy time.

Examples of But I Digress include:

Film

The musical version of this is used in Music and Lyrics, with the song Don't Write Me Off Just Yet, but then again it's Truth in Television that this happens all the time with songwriters, and justified since the girl whose concert it was loves stuff like that and shoehorned it in at the last minute.
Harry Lockhart does this in Kiss Kiss Bang Bang, to much hilarity.
Plot Point #1 in I Love You, Beth Cooper.
Elle's speech to Congress in Legally Blonde 2.
Lampshaded in Mean Girls. Cady is voted queen of the Spring Fling and launches into a talk about how divisive the past year has been and how everybody should get along, which the principal interrupts to point out, "You're really not required to make a speech."
Played straight in Inglourious Basterds when Colonel Hans Landa, in the middle of a conversation that will alter the course of history, pauses to ask his native English-speaking captives if he is properly using the expression "Bingo!"
The end of The American President juuuust about pulls off combining an Anguished Declaration of Love with a political press conference.
Marisa Tomei's scene as an expert witness at the end of My Cousin Vinny, which doubles as a resolution to her lover's tiff with the title character.

Vinny: And because both cars were made by GM... were both cars available in metallic mint green paint?
Lisa: They WUH!
Vinny: Thank you, Ms. Vito. No more questions. Thank you very, very much. You've been a lovely [kiss], lovely [kiss] witness.

Literature

In Dave Barry Slept Here, Thomas Jefferson, who is writing the Declaration of Independence in an all-nighter, lets the document's subject wander to people flushing inappropriate objects down toilets, among other things.
One Polish poet once wrote a cycle of micro-plays and other stories. One of them - that long - includes such a verse: "Unaccustomed as I Am to Public Speaking, let me say, that... (here happens a two-hour-long volcanic eruption of speech, which is completely unrelated to the topic)"

Live Action TV

In Malcolm in the Middle, Malcolm partially does this in the finale with his valedictorian speech before continuing with his planned speech.
In 3rd Rock from the Sun Tommy uses his Valedictorian speech to plead with his exgirlfriend to take him back. When this fails he returns to his original Valedictorian speech "Long Live Rock!"
Cookie Monster says this every once in a while.
The Monty Python's Flying Circus episode "Erizabeth L" has a police inspector (from the Film Fraud Division) who's apparently incapable of arresting a dangerous criminal who's impersonating famous directors without digressing into a lengthy biography of the director in question.

Web Original

The song "All About the Art", in Commentary! The Musical, is only actually about the art for about 15% of its run.

Western Animation

Mocked in an episode of American Dad, where a famous football player was receiving an award in front of a stadium full of people. Said football player was unable to accept his son being gay. Stan dragged his son up on stage and tried to work things out in front of the whole audience. This didn't work at all, but the audience still cheered constantly for no apparent reason (lampshaded with "They'll cheer for anything!").
Happens quite often to Bruce from Family Guy.
- Happens to hilarious effect during Blue Harvest with the "runaway paragraphs in space" as it starts talking about the story but ends up talking about Angelina Jolie in the movie Gia. The narrative then uses this line to get back on subject:

But I digest.

Real Life

People love to propose marriage in wacky, creative ways in public settings. Like at karaoke bar, or on a radio show, or on the billboard at a sports game. Often, they really do get spontaneous applause from the audience.
According to the man himself, author Peter David is so prone to doing this that he called his column in Comics Buyer's Guide, "But I Digress..." as a lampshading of it.