It's a standard rule of video games now that if there's a dog, cat, or other fluffy pet, then, you should be able to pet it. The Elder Scrolls V: Skyrim has been a notable exception - a wrong that is finally righted thanks to this new mod.
The Pet The Dog from modder JaySerpa allows you to pet dogs that you come across within the game world and provides you with three different animations each time you do so - standing, sitting, or lying down.
According to JaySerpa, the animations are not perfect yet and may look a bit odd if you aren't head-on with the dog, but it's a huge improvement over no petting at all, if you ask me. The animations are also best seen in third-person view and may look odd in first-person. Oh, and make sure you put your weapon away before you try this...
The mod relies on Dynamic Animation Replacer, which you can grab here, and the mod itself is available here. Sadly it is limited only to dogs, for now, but hopefully, you'll be able to pet horses, chickens, or random NPCs in the not too distant future? No? Just me then.