For those that have successfully gone off-grid, how many watts?

Yes, My home is all electric ... including heat pump, electric heat, hot water heater ... several computers running 24x7 ... large entertainment center with tons of 'phantom load'.

The 1200kwh, is from before I started looking at it, and trying to change my consumption ... with changing life style.

So far, the only thing I've done to improve consumption, is changing (almost) all of my light bulbs.

I definitely need help, and need to learn more about how to reduce consumption ... again, without changing life style.

Although I have not gone completely "off grid" I can give you some first steps to get there (because I am getting there).
1-conserve--Replace big appliances first (frig, furnace) my 19' cubic Kenmore frig (freezer top) uses only 1 kilowatt a day.  Furnace is high efficiency (96%).  Replace lights with LEDs (porch light is outside in cold so it is LED) CFL's elsewhere.  I converted 20W desk lamps to auto LEDs (www.ledlight.com).  Add plug strips to phantom loads, then switch all of them off at once (until you need them).  If someone tells you "if it ain't broke don't fix it" but your frig is costing more than $3 bucks a month - its broke.  Oh, get newer shower head (low flow/high pressure) and a new toilet, aerators for faucets.
2-smart solar--start with solar hot water.  This is least expensive and gives the most payback.  You use hot water all the time.  Get solar hot air, there are 4 x 8' panels that only need a 6" vent hole (or 2) to install.
3-solar electric--get this after you review your electric bill (with conserve efforts included).  Most off-griders get a gas generator for the winter season but you can save that cash as you have the grid (use cheapest energy first).
Other savings--wood is a good storage medium for heat, get a wood stove (not fireplace) if you have woods near by.

As for the "how many Watts" question? as much as you can afford.  You may have a family and may use more than just me.