As a GGL, the key thing for me is the published benefits- CCR/CCDR access at LHR (I am almost always connecting so use it inbound and outbound), Jokers (a huge benefit for a family), GUFs (again, still a major benefit esp. when travelling in F), and now also Group 0 (especially for Short Haul). Plus all the Gold/OWE benefits (TFW, seat selection, OW lounge access).
Other regular soft benefits are first meal choice in CW and F (usually, but not guaranteed especially on HV routes such as JFK or BOS where F might be full of Prems) and crew greetings (not hugely bothered but I would say a lot of the interaction from crew is made very genuinely and as a "people-person" I do love a bit of a chat).
Other things like car transfers, escorts onto the plane, invitations to events (non-BA and BA) are completely in the "surprise and delight" category for me and most GGLs (GGLfL, GGL+ excepted, I realise). If you don't expect them then you may get a nice surprise now and again.