For the foreseeable future, any domestic installation that could fit your description of "no electric bill" would require a cost per kilowatthour far in excess of the current cost for utility-genereated and -delivered electricity. And when I say "far" I mean "gross excess".
Let's also talk energy management: unless you are willing to lay out $10's of thousands of dollars in upfront costs (that's the plural of 10, not 10) for the generation panels, storage system, inverters, etc. you will have to do two things:
(1) Greatly reduce the amount of electrical energy you consume.
(2) Greatly reduce the electrical power you consume.
Just so we're clear on what this means:
(1) means that you will drastically cut the use of electrical consumers in your home. You will cook with a combustible fuel; you will not leave lights on, even at night; you will unplug your electrical clocks, your DVR that consumes up to 50W 24 hours per day, your cable modem and your router except when you want to use them, your battery chargers, etc. Nothing gets left plugged in unless its being used, and you will focus on using them as little as possible.
(2) means that when you use electricity, you will not draw it out very quickly. You can loosely categorize your biggest power draws as follows:
(a) Electrical stove/oven, electric water heater, air conditioner, electric clothes dryer. These can draw multiple kilowatts, especially the stove/oven, which can pull 10 kw at full power.
(b) Clothes iron, microwave, toaster, toaster oven, coffee maker, hair dryer, some vaccuum cleaners, etc. These are all one kilowatt-class devices.
(c) Everything else. Lights, ceiling fans, televisions, garage door openers, etc.
Both the total energy required and the power crank up the costs. Total energy drives up the cost of the panels and the storage system; total power cranks up the cost of the storage system and the power electronics that convert your stored electricity into something your house can actually use.
It is possible to live off-the-grid with just solar as your generating capacity. It also requires a very, very high up-front investiture which goes up considerably depending upon how reluctant you are to really stop consuming electricity. Long-term maintenance is also a considerable cost, especially for the storage system, and measurements indicate that nearly all photovoltaic systems continually lose some of their generating capacity. In other words, if you installed a 5 kW system (which would be a large system), if might only be 4 kW in 10 years, meaning that you'll need additional panels.
Right now, there's nothing that compares with burning stuff when you want to generate electricity.
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