My favorite is probably a 3-way tie between the 1961 Kenmore 70, the 1963 Kenmore line including the 600, the 70 and especially the Lady K 800s, and the 1976 and later black panel machines.
The 61 is not the most elegant washer, but how could I not love the machine that started it all for me?
The 63s are just plain elegant. I think I like the 70s as much as the 800s, but these are timeless to me. They simply speak "This is what a washer is" to me, nothing more, nothing less.
The 76-86 black panel machines are an entirely different animal to me, but I have a similar feeling about them. I was much older when these came out, was able to actually buy a new pair of my own at the tender age of 21, and I have an awesome fun time rebuilding dozens upon dozens in the 1990s for re-sale. They sold in hours of finishing them, I never had to convince anyone of the Kenmore merits, and they essentially paid for a pick-up truck I bought to haul them. Fun times. Now I am using these machines at home and consider them 'vintage' to a degree and what was once something nearly new that I was selling is now something that people consider old and novelties.
Gordon