My dog's neuter site swollen, black, painful. Is it an emergency?

Poor Quentin! From what I can see in the photo, it does look like he has some swelling and discoloration of the scrotum, and a small amount of bruising around the incision site itself. These issues can sometimes happen after a neuter - they're more common if the dog has been too active (I know this is hard to avoid sometimes!), but sometimes they just happen as a result of the surgery itself, just like post-op swelling and soreness in humans.

If your pup is still eating and drinking normally, and seems alert and otherwise okay apart from being sore and reluctant to move around much, then it would be reasonable to wait until Monday to have him checked out by your regular veterinarian. Do not give any over-the-counter pain medication, as there are no OTC human options that are safe for use in dogs.

In the meantime, you can use a warm compress on the area (a washcloth soaked in warm water, and then wrung out) for 5-10 minutes once or twice a day if he'll let you - this can help some with the soreness, and help the swelling resolve more quickly. I would also restrict his exercise as much as possible (crate rest would be best), since the more he moves around, the more he will aggravate the swelling. Make sure he isn't licking the incision or his scrotum at all, as this will also make things worse - use an e-collar (plastic cone) if needed to prevent this.

If you feel that the swelling and bruising is continuing to get worse over the course of the weekend, or if your pup is not eating or acting extremely depressed/lethargic, then the safest bet would be to have him seen at your nearest emergency clinic to make sure there's nothing more serious going on.