I take "best song" to mean a musical composition that remains in your memory after you've seen the show, especially one written in in any of the many kinds of compact forms we have come to think of as a "song."
So not something that necessarily "works outside" the show, but not something that is a musical sequence or recitative. So, if we were discussing Gypsy, the "best song" would not be "Rose's Turn," but more likely "Some People" or "Everything's Coming Up Roses."
Therefore, I'll exclude "Die, Vampire, Die" from [title of show] because that's really a musical sequence, even though I love the number and its message, and I'll pass on Next to Normal. Even though I love the score, I don't think any of the individual numbers make a "best song" list.
As for musicals in the last 10 years, let's start with Wicked, which turns 10 this fall. I would choose "For Good," which I often find myself singing or thinking about in terms of people in my life.
Also turning 10 is Avenue Q, from which I would choose "There's a Fine, Fine Line," which never fails to move me.
I would add "Lot's Wife" from Caroline, or Change and "Another Winter in a Summer Town" from Grey Gardens. Each of those has come back to me many times since seeing those shows. Also, "I Believe" from Book of Mormon, since the combination of a powerful vocal line and surprising and original humor is an important (and much undervalued) component of musical theater.
And I'll add one song written for "the theater" in that it was written for the show-within-the-show on Smash: "Don't Forget Me."
But, Gaveston, you should not find this thread depressing because you haven't seen or listened to the shows. Why not listen to what people who have seen them and listened to them are genuinely enthusiastic about? Maybe their enthusiasm might open a window in your life.