Mmm, I disagree. While there is no doubt some subjectivity to what feels right in games, certain aspects can absolutely be quantified, as a couple previous responses to my question have shown (thanks guys!). Things like hit-reactions, screen-shake, animation fluidity, sound effects and overall polish to the user experience all effect "feel" in various ways.
Take Little Big Planet vs. any Mario platformer. Many (most?) people will say LBP is a solid series, but few would rank it above Mario platformers in terms of feel. Why is this? Almost certainly it's due to the floatiness and overal imprecision of LBPs controls vs. Marios. Sackboy simply doesn't feel as "right" to control as Mario, despite various other elements in both series than may be better or worse. Another, more personal example, is Diablo III vs. Path of Exile. Many people (particularly here on GAF) hail PoE as the better isometric action-RPG. For me, however, PoE falls flat compared to Diablo III based soley on combat feel. Sure there is a broad and diverse skill tree to level up in PoE, but because the combat lacks the hit-reactions and punch of Diablo III, I feel no compulsion to play the game.
Feel is, in my opinion, absolutely the most important aspect in game design. Without proper feel, there is no reason to play a game.