My (current, yet always changing) list:
1) Bruckner: Symphony #9
2) Sibelius: Symphony #5
3) Rott: Symphony in E
4) Brahms: Symphony #1
5) Schubert: Symphony #8 "Unfinished"
6) Mendelssohn: Symphony #5 "Reformation"
7) Beethoven: Symphony #6 "Pastoral"
8) Elgar: Symphony #1
9) Brahms: Symphony #3
10) Korngold: Symphony in F-sharp
Literal rankings are mostly meaningless, and ten is way too small a sample. Here are my TWENTY favorite symphonies alphabetically. Nothing too exotic here, aside from Nielsen:
Berlioz: Symphonie Fantastique
Brahms: Symphony No. 3
Brahms: Symphony No. 4
Beethoven: Symphony No. 5
Beethoven: Symphony No. 6 "Pastoral"
Beethoven: Symphony No. 7
Bruckner: Symphony No. 4
Bruckner: Symphony No. 9
Dvořák: Symphony No. 7
Dvořák: Symphony No. 9
Mahler: Symphony No. 1
Mendelssohn: Symphony No. 3 "Scottish"
Mendelssohn: Symphony No. 4 "Italian"
Nielsen: Symphony No. 5
Prokofiev: Symphony No 5
Saint-Saëns: Symphony No. 3 "Organ"
Sibelius: Symphony No. 2
Sibelius: Symphony No. 7
Tchaikovsky: Symphony No. 4
Tchaikovsky: Symphony No. 6 "Pathetique"
*Both of Elgar's symphonies are great, and so is the Walton # 1. Shostakovich would probably crack the top 30 and probably a few more Mahler symphonies, too. We both neglected to mention Schubert's Symphony No. 9 "The Great". The only American symphony I would even consider inclusion among the great symphonies would be Barber's one-movement Symphony No. 1.
Heck, why not? The 100 Greatest Symphonies*:
Beethoven: Symphony No. 1
Beethoven: Symphony No. 2
Beethoven: Symphony No. 3 "Eroica"
Beethoven: Symphony No. 4
Beethoven: Symphony No. 5
Beethoven: Symphony No. 6 "Pastoral"
Beethoven: Symphony No. 7
Beethoven: Symphony No. 8
Beethoven: Symphony No. 9 "Choral"
Berlioz: Symphonie Fantastique
Bizet: Symphony in C
Brahms: Symphony No. 1
Brahms: Symphony No. 2
Brahms: Symphony No. 3
Brahms: Symphony No. 4
Bruckner: Symphony No. 4 "Romantic"
Bruckner: Symphony No. 5
Bruckner: Symphony No. 7
Bruckner: Symphony No. 8
Bruckner: Symphony No. 9
Dvořák: Symphony No. 7
Dvořák: Symphony No. 8
Dvořák: Symphony No. 9 "From the New World"
Elgar: Symphony No. 1
Elgar: Symphony No. 2
Franck: Symphony in D Minor
Haydn: Symphony No. 6 "Morning"
Haydn: Symphony No. 22 "Philospher"
Haydn: Symphony No. 26 "Lamentatione"
Haydn: Symphony No. 30 "Alleluia"
Haydn: Symphony No. 31 "Hornsignal"
Haydn: Symphony No. 38 "Echo"
Haydn: Symphony No. 39 "Tempesta di mare"
Haydn: Symphony No. 44 "Mourning"
Haydn: Symphony No. 45 "Farewell"
Haydn: Symphony No. 48 "Maria Theresia"
Haydn: Symphony No. 49 "Passion"
Haydn: Symphony No. 52
Haydn: Symphony No. 82 "The Bear"
Haydn: Symphony No. 83 "The Hen"
Haydn: Symphony No. 85 "The Miracle"
Haydn: Symphony No. 86
Haydn: Symphony No. 88
Haydn: Symphony No. 92 "Oxford"
Haydn: Symphony No. 93
Haydn: Symphony No. 94 "Surprise"
Haydn: Symphony No. 95
Haydn: Symphony No. 96 "The Miracle"
Haydn: Symphony No. 97
Haydn: Symphony No. 98
Haydn: Symphony No. 99
Haydn: Symphony No. 100 "Military"
Haydn: Symphony No. 101 "The Clock"
Haydn: Symphony No. 102
Haydn: Symphony No. 103 "Drumroll"
Haydn: Symphony No. 104 "London"
Mahler: Symphony No. 1 "Titan"
Mahler: Symphony No. 2 "Resurrection"
Mahler: Symphony No. 4
Mahler: Symphony No. 5
Mahler: Symphony No. 6 "Tragic"
Mahler: Symphony No. 9
Mahler: Symphony No. 10 (completed by Deryck Cooke)
Mendelssohn: Symphony No. 3 "Scottish"
Mendelssohn: Symphony No. 4 "Italian"
Mendelssohn: Symphony No. 5 "Reformation"
Mozart: Symphony No. 25
Mozart: Symphony No. 29
Mozart: Symphony No. 35 "Haffner"
Mozart: Symphony No. 36 "Linz"
Mozart: Symphony No. 38 "Prague"
Mozart: Symphony No. 39
Mozart: Symphony No. 40
Mozart: Symphony No. 41 "Jupiter"
Nielsen: Symphony No. 3 "Expansiva"
Nielsen: Symphony No. 4 "Inextinguishable"
Nielsen: Symphony No. 5
Prokofiev: Symphony No. 1 "Classical"
Prokofiev: Symphony No. 5
Saint-Saëns: Symphony No. 3 "Organ"
Schubert: Symphony No. 5
Schubert: Symphony No. 8 "Unfinished"
Schubert: Symphony No. 9 "The Great"
Schumann: Symphony No. 1 "Spring"
Schumann: Symphony No. 2
Schumann: Symphony No. 3 "Rhenish"
Schumann: Symphony No. 4
Shostakovich: Symphony No. 1
Shostakovich: Symphony No. 5
Shostakovich: Symphony No. 10
Sibelius: Symphony No. 1
Sibelius: Symphony No. 2
Sibelius: Symphony No. 3
Sibelius: Symphony No. 4
Sibelius: Symphony No. 5
Sibelius: Symphony No. 6
Sibelius: Symphony No. 7
Tchaikovsky: Symphony No. 4
Tchaikovsky: Symphony No. 5
Tchaikovsky: Symphony No. 6 "Pathetique"
*That's a solid "Top 100 Symphonies".
Another 100 Interesting Symphonies That Didn't Quite Make the Cut (well, 103 actually):
Balakirev: Symphony No. 1
Bantock: Celtic Symphony
Bantock: Hebridean Symphony
Barber: Symphony No. 1
Bax: Symphony No. 1
Bax: Symphony No. 3
Bernstein: Symphony No. 2 "The Age of Anxiety"
Berwald: Symphony No. 3 "Singulière"
Borodin: Symphony No. 2
Bruckner: Symphony No. 3
Bruckner: Symphony No. 6
Chausson: Symphony in B-flat
Copland: Organ Symphony
Copland: Dance Symphony
Copland: Symphony No. 2 "Short Symphony"
Copland: Symphony No. 3
Dukas: Symphony in C
Dvořák: Symphony No. 1 "The Bells of Zlonice"
Dvořák: Symphony No. 2
Dvořák: Symphony No. 3
Dvořák: Symphony No. 4
Dvořák: Symphony No. 5
Dvořák: Symphony No. 6
Glazunov: Symphony No. 1
Glazunov: Symphony No. 4
Glazunov: Symphony No. 5
Gliere: Symphony No. 3 "Ilya Mourumetz"
Hanson: Symphony No. 2 "Romantic"
Harris: Symphony No. 3
Hindemith: Mathis der Maler Symphony
Honegger: Symphony No. 2
Honegger: Symphony No. 3 "Liturgique"
d'Indy: Symphony No. 2
Ives: Symphony No. 2
Ives: Symphony No. 3 "Camp Meeting"
Ives: Holiday Symphony
Kalinnikov: Symphony No. 1
Lalo: Symphony in G Minor
Liszt: Dante Symphony
Liszt: Faust Symphony
Mahler: Symphony No. 3
Mahler: Symphony No. 7
Mahler: Symphony No. 8
Martinů: Symphony No. 1
Martinů: Symphony No. 2
Martinů: Symphony No. 3
Martinů: Symphony No. 4
Martinů: Symphony No. 5
Martinů: Symphony No. 6 "Fantaisies symphoniques"
Mendelssohn: Symphony No. 1
Mendelssohn: Symphony No. 2 "Lobesgesang"
Nielsen: Symphony No. 1
Nielsen: Symphony No. 2 "The Four Temperaments"
Nielsen: Symphony No. 6 "Sinfonia semplice"
Prokofiev: Symphony No. 6
Rachmaninoff: Symphony No. 1
Rachmaninoff: Symphony No. 2
Rachmaninoff: Symphony No. 3
Rachmaninoff: "The Bells" Choral Symphony
Rimsky-Korsakov: Symphony No. 2 "Antar"
Roussel: Symphony No. 1 "Poem of the Forest"
Roussel: Symphony No. 2
Roussel: Symphony No. 3
Roussel: Symphony No. 4
Scriabin: Symphony No. 1
Scriabin: Symphony No. 2
Scriabin: Symphony No. 3 "Divine Poem"
Scriabin: Symphony No. 4 "Poem of Ecstasy"
Scriabin: Symphony No. 5 "Poem of Fire"
Shostakovich: Symphony No. 2
Shostakovich: Symphony No. 3
Shostakovich: Symphony No. 4
Shostakovich: Symphony No. 6
Shostakovich: Symphony No. 7 "Leningrad"
Shostakovich: Symphony No. 8
Shostakovich: Symphony No. 9
Shostakovich: Symphony No. 11
Shostakovich: Symphony No. 12
Shostakovich: Symphony No. 13 "Baba Yar"
Shostakovich: Symphony No. 14
Shostakovich: Symphony No. 15
Sibelius: Kullervo Symphony
Stravinsky: Symphony in C
Stravinsky: Symphony in Three Movements
Stravinsky: Symphony of Psalms
Suk: Asrael Symphony
Tchaikovsky: Symphony No. 1 "Winter Dreams"
Tchaikovsky: Symphony No. 2 "Little Russian"
Tchaikovsky: Symphony No. 3
Tchaikovsky: Manfred Symphony
Vaughan Williams: Symphony No. 1 "A Sea Symphony"
Vaughan Williams: Symphony No. 2 "A London Symphony"
Vaughan Williams: Symphony No. 3
Vaughan Williams: Symphony No. 4
Vaughan Williams: Symphony No. 5
Vaughan Williams: Symphony No. 6
Vaughan Williams: Symphony No. 7 "Antarctica"
Vaughan Williams: Symphony No. 8
Vaughan Williams: Symphony No. 9
Walton: Symphony No. 1
*and another 22 Haydn symphonies worth hearing... 52 out of 106 total symphonies
Haydn: Symphony No. 7 "Afternoon"
Haydn: Symphony No. 8 "Evening"
Haydn: Symphony No. 13
Haydn: Symphony No. 14
Haydn: Symphony No. 34
Haydn: Symphony No. 43 "Mercury"
Haydn: Symphony No. 47 The Palindrome"
Haydn: Symphony No. 53 "L'impériale"
Haydn: Symphony No. 55 "The Schoolmaster"
Haydn: Symphony No. 59 "Fire"
Haydn: Symphony No. 60 "The Distracted"
Haydn: Symphony No. 63 "La Roxelane"
Haydn: Symphony No. 64 "Tempora mutantur"
Haydn: Symphony No. 69 "Laudon"
Haydn: Symphony No. 73 "The Hunt"
Haydn: Symphony No. 80
Haydn: Symphony No. 81
Haydn: Symphony No. 84 "In nomine Domini"
Haydn: Symphony No. 87
Haydn: Symphony No. 89
Haydn: Symphony No. 90
Haydn: Symphony No. 91