Of course, this is very difficult to do since I like just about everything that Mr. S ever did in the recording studio. If I had to narrow it down, here's my list:
ALBUMS:
1) IN THE WEE SMALL HOURS OF THE MORNING (1955)
2) SONGS FOR SWINGIN' LOVERS (1956)
3) SEPTEMBER OF MY YEARS (1965)
4) A MAN AND HIS MUSIC (1965)
5) SHE SHOT ME DOWN (1981)

SONGS:
1) DON'T WORRY 'BOUT ME (1953)
2) ANGEL EYES (1958)
3) HERE'S THAT RAINY DAY (1959)
4) COME RAIN OR COME SHINE (1961)
5) I HAVE DREAMED (1963)

I sure did leave a lot of great stuff off this list, but as we all know, music is VERY subjective and open to all sorts of criticism, both positive and negative. I'll go with my choices above; however, PLEASE don't overlook the "early" Sinatra from 1939-1952.
".....when Sinatra paints a portrait, the tones and colors are his alone." ~Sid Mark~

Yes, the question is asked very often, and with each time, it becomes the more difficult to answer... anyway, here are mine (with the exception of "Lonely Town" being my all-time-favourite Sinatra recording of ALL, the sequence doesn't necessarily mean a rating):

Albums:
1) In The Wee Small Hours (Capitol, rec. 1955)
2) September Of My Years (Reprise, rec. 1965)
3) Moonlight Sinatra (Reprise, rec. 1965)
4) Swing Easy (Capitol, rec. 1954)
5) Frank Sinatra Sings For Only The Lonely (Capitol, rec. 1958)

... and ALL the other albums by Frank Sinatra, who was the album master!

Songs:
1) Lonely Town (Capitol, rec. 1957, Album "Where Are You?")
2) Send In The Clowns (duet w/Bill Miller, piano) (Reprise, rec. 1976, Single)
3) River Stay Away From The Door (Capitol, rec. 1960, Single)
4) Just As Though You Were Here (Reprise rec. 1974, first issued in 1990 on "The Reprise Years")
5) I've Got You Under My Skin (Capitol, rec. 1956, Album "Songs For Swingin'Lovers")

... and ALL the other roughly 1300 studio recordings made by Sinatra, who was the master of song interpretation! (Well yes - EVEN "Mama Will Bark" has its moments... uh, err, well... *g*)

The one Sinatra recording to which I have the closest "emotional ties" so to speak is "Lonely Town"... the musical and vocal beauty of this genius collaboration of FS and Gordon Jenkins is so captivating that it still brings tears to my eyes upon each listening, even today, more than 25 years since I first heard it, and after possibly a thousand or so listenings. Oh boy... what craft. Thank you, Francis.

Bernhard.

In The Wee Small Hours
Point Of No Return
Songs For Swingin' Lovers
Sinatra And Strings
Sings For Only The Lonely

Ted deCerchio
Frank S. once said on Man & His Music special that to pick his favorite songs is like choosing between steak & ice cream.Yet his songs are more enduring than these cholesterol specials.I would go by composer: A Man Alone entire album of Rod McKuen;Michel Legrand songs especially The Saddest Thing of All;Johny Mercer I Thought about you,Emily,When the World Was young;Ted Koehler Don't Worry 'Bout Me,Ill Wind;Sammy Cahn with Jule Styne I've Heard That Song Before,Time After time,,It's the Same Old Dream;with jimmy Van Heusen The Second Time Around,Call Me Irresponsible,All My tomorrows(original),(song)Only the Lonely, I Like to Lead When I Dance;Johny Mandel Shadow of Your Smile,Emily;Jimmy Webb Phoenix,This Time;
& songs whose composers escape me now,like Blame It On My Youth,With every Breath I Take(Close To You is my album choice),More,To Loved & Be Loved,entire All Alone album of primarily Irving Berlin songs. Finally, Frank's favorite song acc. to The New Yorker was Indiscreet,was played by Bill Miller @ Frank's Funeral & not a dry eye in the Church.