Pet and horse replacements
From the same modder that brought you lightsaber swords and a Yoda Wizard on the previous page comes a mod that changes your cat or dog into BB-8. I don't really think I need to say more, because this is probably one of the greatest things ever to be modded in to Stardew Valley. It's hard to make a spherical robot out of small squares, but JG Mods manages it pretty well.
Modder WildSpirits has started a series recolors for Stardew's three pets: the cat, dog, and horse. This is a very light-touch mod, specifically aimed at adding new breeds of each animal to the game, and you can download whichever specific ones you would like while skipping the alternatives. Pet Replacements currently has Border Collie and Pug skins for the dog, Calico and Siamese skins for the cat, and Painted and Blue Roan skins for the horse. More are on the way, and other breeds like this Shiba Inu have already been made by different modders, but this definitely a mod pack to keep an eye on as it grows.
Annoying Dog from Undertale
Modder FinalMantasyX has entirely swapped the pixel sprite for the regular dog with the Annoying Dog from Undertale. It's a brilliant little mix of pixelated indie hits, and an oddly appropriate reskin for one of Stardew Valley's pets. As of now, the game's cat and/or dog have no impact on gameplay, and generally just run around getting in your way—most notably the they can do so when you are trying to place a building for construction, allowing the Annoying Dog to remain true to its name in Stardew Valley as well. Next up, running around my farm with this song playing on a loop.
If you want to make sure your lovable horse companion is way more unsettling than ever intended, modder Giambro has got you covered. Ride around town on a skeletal demon horse instead of the boring old living kind. It even breathes fire when you leave it sitting in the stable!
The cat and dog aren't the only ones that get pop culture replacements, as modder NachoDevs has replaced the horse with a chocobo from Final Fantasy. Once again, this is just a visual replacement, and unfortunately this song won't play automatically as you ride around town, but you can be sure I'll be whistling it the whole time I'm riding mine.
And finally, why ride an animal to get around anyway? That seems pretty old fashioned when you think about it, so don't think about it and instead cruise around your farm in a tractor. Sure, you're still putting it to sleep in the stable you built for a horse, but who cares when you can ride around town in luxury. This tractor mod is pretty hilarious, but it also manages to fit into Stardew's style pretty well, which is an achievement seeing as modder Pewtershmitz had to make it from scratch.