Harmonious Claptrap

Background
This is the vanity card of Dan Harmon (creator of Community and co-creator of Rick and Morty).

1st Logo (December 2-9, 2013)
Logo: On a background, we see a painting of Dan Harmon with a big  cat on his lap and beside him is the company name written in white.

FX/SFX: None.

Music/Sounds: On "Pilot", the closing theme. On "Lawnmower Dog", the sound of ice cubes into a glass.

Availability: Seen on the first two episodes of Rick and Morty.

Legacy: This logo is likely a placeholder for the next logo. Sadly, this logo was only used twice. Harmon and his cat are quite charming.

2nd Logo (December 15, 2013-October 4, 2015)
Logo: On a black background, we see clay models of Dan Harmon and his ex-wife Erin McGathy with a cat in her lap, and a dog beside Harmon in a living room watching TV complete with a rug on the floor, a table lamp next to Harmon and a behind them a shelve with pictures. Above them is the company name written in a childish font.

FX/SFX: The TV flickering.

Music/Sounds: Dan Harmon saying "Did you get any of that?".

Availability: Seen on the first two seasons of Rick and Morty (excluding the first two episodes of the series, since they used the previous logo) and the final season of Community.

3rd Logo (July 14, 2016-October 20, 2019)
Logo: On a black background, we see the same model of Dan Harmon (but now with a plaid shirt and jacket), lying on the chair with a dog and a kitten and holding a bottle of liquor. Next to Harmon are two additional liquor bottles, with a pile of crushed beer cans next to his dog, who is now looking at the viewer. The same words in the same font (albeit a little wider) is above.

Trivia:
 * Erin McGathy, Harmon's ex-wife, designed this logo (per Harmon's request) after the two divorced. According to McGathy, this was the second draft of the vanity card, feeling that the original "wasn't sad enough." Despite this, McGathy holds no hard feelings: "I'm happy to see the model has become happy again with the most recent vanity card. :)"
 * McGathy eventually sold the model for this vanity card to a private buyer, with proceeds going to MOB Theater Dublin. There used to be behind-the-scenes shots of the logo on her website, but sadly, the page is down.

FX/SFX: Same as the 2nd logo.

Music/Sounds: Same as the 2nd logo.

Availability: Seen on HarmonQuest and the third season of Rick and Morty.

4th Logo (November 10, 2019-)
Logo: On a black background, we see Dan Harmon (with a beard and a different plaid jacket) and his new partner, Cody Heller, asleep in bed, with two dogs on the bed, both of them also asleep. There are two lamps, one to the left and another to the right. Again, the words are in the same font as above.

Variant: On Little Demon, the logo is still and shares the screen with the Jersey 2nd Ave and Evil Hag Productions logos.

FX/SFX: Same as the last two logos.

Music/Sounds: Same as the last two logos, or the closing theme of the show.

Availability: Seen on the fourth, fifth, and sixth seasons of Rick and Morty and Little Demon. It is expected to appear on Dan Harmon's upcoming series such as Krapopolis, Strange Planet, and Chuck Deuce. Don't expect to see this logo on Vindicators 2: Last Stand Between Earth and Doom (a spinoff of Rick and Morty), despite Dan Harmon being one of the executive producers on the show.

Legacy: As previously mentioned, Harmon's new marriage means that this is much happier than the third logo.