My wife, two kids and I live "off grid" in upstate NY with all of our electric needs supplied by a 1400+ watt solar array and battery storage. The initial cost of our system was comparable to bringing in grid power so we could have gone either way. We liked the idea of our own on site system, and a limited amount of power which would force us to use electricity as though it wasn't an unlimited resource. We also get many power outages around these parts and liked the advantage of never having one ourselves.
That said, I'll be the first to vouch for the fact that it isn't cheap. The system cost is a deep investment, and if you plan on making your house as efficient as possible so that you don't gobble up all you power you're in for many related expenses. We ran two strands of wire throughout the house to provide ac as well as dc outlets. Our lighting is all dc and the bulbs aren't cheap. Our submersible is dc and it's cost is much more than an ac model. The high efficiency dc ceiling fan cost a couple times more than a standard ac and the variable speed switch wasn't includes (that cost as much as a ac fan). And the dc refrigerators? I'll just say that after 6 years on our system I still can't bring myself to write the check though we do have a standard ac fridge. We did recently double the size of our solar array and upgrade our charge controller which further increased the efficiency of our system and received a 55% rebate between federal and state incentives.
I won't bother trying to figure out when I'll break even. I doubt it'll ever happen. Electricity isn't that expensive here and if your on-grid house is as efficient as ours your bills would be negligible. I live in the woods though and being off grid contributes to my sense of self -sufficiency just as my wood stove does. (the labor I put into firewood if put into my trade would pay my heating bills many times over).
I have to point out that the life of the system - even the batteries - is much longer than what some folks think. The components are all solid-state, the solar panels have a twenty year warranty and my batteries - all deep cell lead acid - are holding as much power now as they did 6 years ago. I have friends who have the same batteries they installed 20 years ago. Keeping them charged properly and well cared for will keep them healthy for many years. Change the oil on your car every 4k miles? Water your batteries every two months. As far as generator use goes, that is up to the system user. I know folks who want to live off-grid as though they're on-grid with no concern for the amount of power they consume, and they run their generator every day during the "dark months", while others who when their storage is getting low adjust their consumption so they never have to run a generator.
As for ourselves we're doing laundry, watching tv, listening to the stereo, using the computer just like the rest of you or maybe even more so. One big difference is that to some extent we keep our eyes on the meter between October and January. If the battery bank is approaching 60% we'll maybe hold off doing 3 loads of laundry in one day, or if there's no chance for sun for days ahead we'll charge up to 100% with the generator (a honda 5000 watt). That takes around 5 hours. This is based on our 1/2 array. With the upgrade those days will be far fewer if at all.
We're definitely not living an austere existence here. We do turn out lights when we're not using a room and the tv isn't on all day long as background sound, but I have a wood shop and I'm regularly running my table saw, chop saw, and other equipment as well as doing a fair amount of mill work. I've never been unable to run this equipment nor have had to run the generator to work in my shop. And I'll point out again that I live in upstate NY, due East of the Great Lakes. Sunny Arizona it ain't. Now if I lived there I might try to figure my break even point.