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)
Visuals: On a background, there is a painting of Dan Harmon with a big  cat on his lap and beside him, the company name written in white.

Technique: Traditional oil paint.

Audio:
 * 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.

2nd Logo (December 15, 2013-October 4, 2015)
Visuals: Over a black background, there are some 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, there's the company name written in a childish font.

Technique: Claymation.

Audio: A slightly muffled voice clip of Dan Harmon saying "Did you get any of that?", presumably through a recording booth.

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)
Visuals: On a black background, there is the same model of Dan Harmon (but now with a plaid shirt and jacket), lying on a 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) are 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.

Technique: Claymation.

Audio: Same as the 2nd logo.

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

4th Logo (November 10, 2019-)
Visuals: Over a black background, there's 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 and Strange Planet, the logo is still. On the former, it shares the screen with the Jersey 2nd Ave and Evil Hag Productions logos.

Technique: Claymation.

Audio: Same as the last two logos, or the closing theme of the show.

Availability: Seen on Rick and Morty starting with its fourth season, Little Demon, Strange Planet, and Krapopolis. This logo does not appear 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.