Technically, the most favourited cache I have logged is Geocaching HQ. However, I will not count it here since I haven't actually visited the inside of the HQ, just signed the log book. It was available for signing at the Block Party I attended in 2015. Here are the three that comes next.
GC31EQD Töff Töff für das Kind im Manne (und Frau :-) ) Nordrhein-Westfalen, Germany 3901 FP
Fantasic cache, unfortunately it was not working properly when I was there and a little while later it was archived.
Another one, still active, is probably on many statistic hunters lists. It is the second oldest cache in Europe.
GC40 Geocache Namur, Belgium 3587 FP
Then of course, there is this one, a real classic.
GCGV0P Original Stash Tribute Plaque Oregon, USA 3325 FP
When I got there, another cacher was just leaving. He had driven across the country from New York...