George,
IFR and VFR are rules...hence the name...Instrument Flight Rules or Instrument Flight Rules. These rules cover the amount of fuel that must be covered, distances from clouds, weather minimums, etc. VFR and IFR are also types of flight plans, or in other words, flight plans specific to the operating rules.
Airlines operate under IFR. A visual approach is an IFR procedure, though it may not be an insrument procedure. One can operate IFR is clear visual conditions...and one frequently does. IFR places on in the airspace system, participating in radar traffic separation, etc.
I don't know about other operators, but the operations I've worked for (and currently work for...until the upcoming furlough) require us to fly under IFR, with an IFR clearance, on an IFR flight plan. We're allowed to depart VFR and pick up a clearance in the air, so long as it's done within 50 miles, and we can cancel a flight plan and land under VFR when within 35 miles of the airport. Different operators have different requirements. As a general rule, we don't do either one.
In the case of a visual approach, if the airport is served by an instrument approach, we fly the approach, and always at altitudes above those prescribed for the approach that serves the runway. It's perfectly acceptable to fly visually to the runway and land, and we sometimes do, but the procedures for the runway gaurantee obstacle clearance and a stable approach, and where they're available, we follow them...whether we're flying by automation, or hand flying.
I frequently fly approaches by hand, as often as flying them on automation.