I voted for "Saying Goodbye," simply because it epitomizes one of the problems I've always had with TMTM - the concept of the Muppets breaking up (although I realize that's partly what drove the new movie). The fact that it resurfaced in the media coverage of Jim Henson's death only cements the heartbreaking nature of the song, even though it's a good song.
A couple of weeks ago my aunt was given a 10 per cent chance to live and the entire family flocked to her hospital bed - I was stuck at work and found "Saying Goodbye" on YouTube...I almost lost it right in the middle of the office. (Fortunately, my aunt is doing much better now and we're hoping she will be able to have the surgery she needs within a matter of days. But I digress...)
"When Love Is Gone" is pretty sad too, but "Pictures In My Head" actually has a hopeful sound to it when the other Muppets join Kermit and they all musically muse about the thought of getting together again.
I'm genuinely surprised to find "I'm Going To Go Back There Someday" in this poll. I know it comes at a sad part of TMM (the Studebaker breaks down, the Hollywood dream looks dead and Kermit feels like he dragged everybody into a mess) but the lyrics strike me as hopeful and optimistic. This has been a favourite song of mine for many years (I've sung it at a handful of public music performances too) and I liked that one of the regular posters here teamed it up with Jesus' scriptural self-description as "the way, the truth and the life" - I think it has Christian overtones without specifically mentioning God. A neat musical trick, I must say...
Also, I never considered "Bein' Green" to be sad - it can actually be very empowering if you listen to it in the right frame of mind; it's quite an uplifting song on a sad day.