For general odour remover, I use Stink-Free candles (I'm prone to the butterscotch and the executive aromas). For basic furniture/carpet odour removal I use Nok Out. For specific messes I use Nature's Miracle Just For Cats for cat pee, Simple Solutions Stain and Odour remover for dog pee and all other messes (I've used it for poop, vomit, blood, ink and wine). For really bad carpet issues I pull the carpet up and spray Get The Odor Out on the underpad and the back of the carpet - full strength. For the bird cages we use Simple Solutions Bird Droppings Remover.
I'm very curious to learn what everyone else uses!
Oh, for general cleaning we have always used just hot water with a touch of bleach or warm water with a touch of Orange-a-Peel. We don't use chemicals or anything strong because of the special needs critters who can't tolerate much of anything that is too strong or artificial.
For the record, we currently have five dogs, two cats and five parrots in the house. However, we have topped out at 6 cats + 13 dogs, and 22 cats + 3 dogs (different occasions). We run a rescue, so these were emergency situations that lasted about a month or so and then tapered down quickly.
One final note - for cat litter we use a pair of kiddie pools in the basement filled with Feline Fresh pine litter. They're a bit of a challenge to clean, but litter box odour is nonexistent in my home - even when the cats numbered 22.

Good food all around also keeps the odour under control - as does regular baths for the dogs and showers for the parrots. We spend a LOT of time cleaning. But they're worth it.
