My current camera set-up for wedding photography:

Nikon D750 + 24-70mm

I use all full-frame format D-slr’s, as you never know what the lighting is going to be like at a church or venue. Larger format cameras tend to hold up better in low light venues. 

I use two Nikon D750’s, one with a standard zoom and the other with a fixed prime lens, this gives me redundancy if one of the cameras fails for any reason I can quickly switch to the other. I use the zoom for versatility, enabling me to get different looks of the same scene, close and wide. The prime lens on my other camera is mainly for the artistic shots. 

I have a couple of flashes in my bag just in case its a really dark venue, however I try to avoid using them if I can. Capturing ambient light will sometimes introduce grain into photos but it will also produce more natural images you will have remembered experiencing on the day. Photography is all about compromises, we work with whats available and do the best we can.

That’s about it really. I try to keep things simple and it seems to work!