Great topic--not necessarily the "best" but the most played.
1) Rain Dogs by Tom Waits. This is probably most people's intro to Waits. It was 1991, and I was 17 and a senior in high school. In a time before internet when some of us were vainly trying to seek out something truly special, this was a godsend.
2) Pod by The Breeders. I've listened to every Pixies album over and over, including b-sides. I still haven't listened to them nearly as much as their bass player's (Kim Deal) first foray as a front person. For those who follow studios/producers/technicians, this was done in Steve Albini's studio. He considers it one of his best studio efforts, for what it's worth. It's sort of a dreamy post-punk cross between Pixies and Throwing Muses. I had to listen to it many times before I realized I liked it let alone LOVED it.
3) The Facts of Life by Black Box Recorder. If you like the dream-pop sub-genre of brit-pop, it doesn't get any better. I accidentally left this in my mother's travel agency one day, and she and her boss listened to it for days. They also never tired of it. I don't know what it is, but it never feels over-played.