Looking at a list of albums released in 1966:
Simon & Garfunkel - Sounds of Silence: My sisters were big fans, so I heard a lot of "Si and Gar" as a kid, and I am generally a fan of their music (although I don't own this album).
Beatles - Yesterday and Today and Revolver: Y&T was a compilation album of a bunch of singles, some of which are on Rubber Soul and Revolver. Highlights for me are Nowhere Man, Yesterday, We Can Work It Out and Day Tripper. Revolver is a great transitional album for the Beatles. Taxman is probably the first great George Harrison Beatles song. Eleanor Rigby, Here, There and Everywhere, She Said She Said, And Your Bird Can Sing, For No One, and Tomorrow Never Knows are my favorites. Day Tripper and Paperback Writer were also released as non-album singles (the former as a double A-side single with We Can Work it Out, and the latter with the criminally underrated Rain as the "B-side").
Not too much else of interest for me, although The Who's A Quick One featured a couple of John Entwhistle classics: Boris the Spider and Whiskey Man (the latter of which features The Ox on French horn, as well as lead vocals).
The Yardbirds released Shapes of Things, and the Mamas and the Papas released California Dreamin', both of which I like a lot. Also Summer in the City by the Lovin' Spoonful.