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.

The favourite songs change every day, but two that always comes to mind are "I've Got You Under My Skin" and "Angel Eyes".

"In the wee Small Hours" has been my favourite album for quite some time, although there are several others that are almost just as good., of course. I recently had to buy a new copy of the CD, as the old one stopped playing in the middle of "When Your Lover Has Gone".

"You make me feel so young......."

Songs for swingin lovers is the album for me and the single I like the most is on this album..."It happened in Monterey".

i share the same song with my stepdad. summer wind

Albums
1)Moonlight Sinatra (Utter Perfection, to only be listened to on a dark moon filled night)
2)She Shot Me Down (Loved LA is my lady, but this was the final masterpiece, this was rawr Saloon album stuff)
3)A Man Alone (Unlike any other album ever, and is the epitome of a concept album)
4)Sinatra and Strings (Packed full of American standards, and the best ever sung Album, in the world ever.)
5) Sinatra and Swingin' Brass (So beautifully punchy, and sexy, something that was taken to a new level in the Base albums.)

Songs

There are so many to choose from, but as I write this a few come to mind; in no particular order.
1)I've been to town
2)The Single Man
3)Don't take your love from me (1961 version)
4)More
5)Moonlight Moon
6)Oh You Crazy Moon
7) Don't Worry Bout' Me (1966 version)
I'll only miss her when I think of her
9) South to a warmer place
10) Gal that got away/Never entered my mind Medley (Possibly the greatest recording of the 20th century?)

"Swing Easy" on Capitol
"I Remeber Tommy" on Reprise
"Love Is A Kick" on Columbia
"In The Wee Small Hours" on Capitol
"The Voice" on Columbia

Favorite LP: 'Where Are You' because of the lush arrangements of Gordon Jenkins and Frank's cello like vocal styling.
Favorite Song: "If I Only Had A Match" because of Frank's gentle swinging of the lyric.
Of course there are other albums and songs, but they are too numerous to count.