Even those mentioned above have one or two mediocre, if not klunker, songs in them.
I'd say, maybe, "Guys and Dolls", though I can't even say I love "Marry the Man Today" or "Sue Me"... but that's the closest I can think of off the top of my head..
Plenty. These are shows that I think don't have a bad song in the sense that they are well crafted and fit perfectly into the show (in addition to the fact that I enjoy the hell out of them): Show Boat, No No Nanette (these don't so much fit into the show, but it's one of the most enjoyable scores ever), South Pacific, Finian's Rainbow, Kiss Me Kate, My Fair Lady, She Loves Me, Gypsy (I love "Little Lamb," shoot me), Little Me, A Little Night Music ("Liaisons" is a fantastic song, some actresses just don't do it justice), Sweeney Todd, A Chorus Line, Nine, City of Angels, Crazy For You (yes it counts), Ragtime, The Full Monty, Caroline or Change, and Next to Normal.
Some honorable mentions: Great scores that have a song in them I don't like, but many seem to enjoy: Carousel ("Highest Judge of All"), On the 20th Century ("I Rise Again"), Follies ("One More Kiss"), Evita ("Art of the Possible"), Les Miserables ("Little People"), Light in the Piazza ("The Joy You Feel"), The Book of Mormon ("I Am Here For You"), and Grey Gardens ("Marry Well")
"Sing the words, Patti!!!!" Stephen Sondheim to Patti LuPone.
The first two that immediately came to mind were Gypsy and Sweeney Todd. West Side Story is pretty solid too, if you look at Krupke as a song and ignore its placement.
Nine Gypsy Parade Evita Les Miz Into the Woods Merrily We Roll Along Sunset Blvd. Pal Joey The King and I City of Angels On the Twentieth Century Sweet Charity Cabaret (the original, but even more so the 54 revival) Fiddler on the Roof Hallelujah Baby Shenandoah Little Shop of Horrors The Rocky Horror Show The Sound of Music Flower Drum Song Guys and Dolls West Side Story A Chorus Line Annie Rags The Apple Tree (Even the cut song "I'm Lost" is a keeper) Hair The Last 5 Years Grey Gardens
And if revues count:
Closer Than Ever Ain't Misbehavin Sophisticated Ladies
Special mention:
Hot Mikado
And finally a brilliant score with one song that I don't care for:
The Light in the Piazza (Aiutami being the one song I dislike)
I'm confused by your question. There are countless scores which have absolutely no "bad" songs in them. Are you asking about scores in which songs are without exception great?