What breed of rabbit is this?

That is not a wild rabbit, it is a domestic and should be caught and properly cared for.
It is, perhaps, an English Spot or Checkered Giant. Never the less, it is a feral domestic. Wild rabbits are always of an Agouti color ( brown with ticking. )
These coat patterns can be brown ( Agouti, wild coloring) blue, black, gray, lilac, even orange.

www.rabbitmatters.com/english-rabbit.html

What breed? Without knowing the exact size of the rabbit you’re seeing in the yard, it could be a Dutch, Mini Lop or a Mini Rex.

Anywho, as @Coloma said, this is not a wild rabbit. It’s domesticated. Someone’s pet is on the loose in your backyard. You may want to post photos around town.

www.bunnyhugga.com/a-to-z/breeds/checkered-giant.html

@SpatzieLover Yes, mini-lop too..I used to know all my rabbit breeds better, my daughter raised Tans and Red New Zealands and we also had a french Lop.

Yes, it is either a Checkered Giant or English Rabbit.

Next question is what we should do about it. Taking pictures of it is very difficult as the rabbit is very fast.

Not a lop because the ears are pointy.

@weeveeship If it is really feral the best you can do is rent a humane trap and try to bait it with something irresistible, like a bunch of alfalfa hay. Rabbits love Alfalfa, or Timothy Hay. You can buy small bales in the pet store. It smells really fragrant and might attract it to the trap.

It would probably tame down if kept in captivity again but do not risk trying to handle it in case of a bite.
The odds of it surviving for very long are not great, especially if you live in an area with wildlife such as foxes and coyotes or bobcats. Dogs too.
You could also use sliced apples as bait but the hay would send out a much stronger scent.

As much as I find the rabbit somewhat interesting looking, I do not have the time or interest in raising it.

@weeveeship You don’t have to keep it, but, if you were interested in trying to trap it, it might find a good home. I am sure there are rabbit rescue groups in your area, maybe do some research and someone would try to trap it.

My dad built a few traps for rabbits. They aren’t difficult. Or, I think you can buy one, quite cheaply. I remember sticking the hunk of apple on the spike on the inside of the trap. http://www.animaltraps.net/animaltrap/rabbit-traps.html Please have a go at trapping it and making it a semi-pet if not for you, than for someone else. It’s colouration makes it an easy target in the wild.

Interesting twist: It appears that the rabbit is in fact a pet. It appears to belong to one of my neighbors (I saw my neighbor playing with it) and for some reason comes over to our yard from time to time.