"By definition, off-grid or stand alone systems are systems where electrical power is generated and stored without assistance from the utility grid. These systems typically consist of one or more power generation sources such as a PV array, a wind generator, a hydro-electric generator or a gas powered generator." -- sma america 4248u manual
one can also (and I am personally referring to) being off-grid in other ways... using less of the connected systems.. the sewage system, the stormwater system, the water supply system, the waste management system, etc. through methods such as rainwater collection, alternate diversion, composting, recycling, reuse, etc.
however, I am also not totally or militantly anti-grid in any way. There are big benefits to being part of the grid such as being able to sell excess power/capacity back to the grid, and being able to get needs met that one cannot provide themselves.
As far as the phone system (dsl, isdn, dialup), cable (internet), etc. one does not pay for a level of power usage -- only for the service and/or access. one can also get online through various means -- local free wifi, amateur radio/packet radio, etc. and be totally energy independent.