Main Canon
----------

Within the main canon there are no examples of the Borg successfully assimilating anything other than [sentient, bipedal, humanoid creatures][1].

That being said, there's no reason to assume they *couldn't* assimilate them, if the mood took them and they saw a benefit in doing so. Otherwise they'd just **ignore them or kill them if they presented a threat.**

EU Canon
--------

Within the novel [The Return][2] (written by none other than William Shatner) PIcard encounters some **assimilated dogs**

> Two dogs—sleek Dobermans, pets of the personnel who had been assigned
> here, no doubt, trotted past. But they did not stop to investigate.
> **Bioneuronic implants studded their skulls. Biomechanical tubes were
> grafted to their chests.**
> 
> One dog turned to look at Picard as it passed. One eye clear though
> expressionless, so unlike the breed. **The other eye had been replaced
> by a laser sensor.**


  [1]: http://scifi.stackexchange.com/questions/20274/why-are-there-no-non-humanoid-borg?rq=1
  [2]: https://en.wikipedia.org/wiki/The_Return_(Shatner_novel)