Can large aircraft go VFR?
The FAA treats large airplanes the same as any other airplane when it comes to VFR flight.  They are required to maintain the same distance from clouds, only fly with the same minimum visibility, see and avoid other aircraft, etc.  

However, since only IFR flights are allowed above FL180 (without a special exemption), and large turbine airplanes are terribly inefficient at low altitudes, so it doesn't happen very often.

In the US, Part 121 flights have the most restrictions of any of the operating rules, and they have multiple regulations relating to VFR flight, including this one1:


  14 CFR 121.611 Dispatch or flight release under VFR.  
  
  No person may dispatch or release an aircraft for VFR operation unless the ceiling and visibility en route, as indicated by available
  weather reports or forecasts, or any combination thereof, are and will
  remain at or above applicable VFR minimums until the aircraft arrives
  at the airport or airports specified in the dispatch or flight
  release.


So yes, even if it is operated by a 121 carrier, they are allowed to fly VFR by the regulations.  However, they must also comply with their Operations Specifications and Flight Operations Manuals which will have detailed procedures covering the conditions where it is allowed.

Outside of 121 there are even fewer restrictions on VFR flight. 



1 There is also:


§121.347 - Communication and navigation equipment for operations under VFR over routes navigated by pilotage.
§121.349 - Communication and navigation equipment for operations under VFR over routes not navigated by pilotage or for operations under IFR or over the top.
§121.649 - Takeoff and landing weather minimums: VFR: Domestic operations.
§121.667 - Flight plan: VFR and IFR: Supplemental operations.