For me, the frame (and sometimes fork) define what makes "a bike". Sure, changing the wheels, cockpit and drivetrain can make it feel different from the way it was previously configured, but the geometry and character of the frame is what forms the basis of "the ride"
Maybe it's because I tend to gravitate to bikes that are a little outside the normal.
My Cannondale and Softride bikes, I chose because they don't ride or handle like more common bikes. They've both been updated over the years (especially the Softride) but that just enhances what makes them stand out in the first place