I haven't played every game, but I would think there would be some form of music in them. I know in TP it was small but you still howled as a wolf and played the grass in human form. There are musical instruments of some variation in all the games that I have touched.
That's ALMOST true. Here we go:
LoZ: Whistle/Recorder
AoL: Whistle/Recorder
ALttP: Flute
LA(DX): Ocarina
OoT: Ocarina
MM: Ocarina
OoA: Harp of Ages and Strange Flute
OoS: Strange Flute
WW: Wind Waker
FS: N/A
FSA: N/A
MC: Ocarina of Wind
TP: Howling Stones/Grass
PH: N/A
ST: Spirit Flute
The only games completely missing it are the FS games and PH. Kind of a shame, though... they were really close to having one in every game.
Here's my list of things that actually are in all the Zelda games:
1. Keys
2. Heart Containers
3. Sword
4. Fairies (three accompany you in PH but are called spirits, and they can be summoned by the Song of Healing in ST dungeons)
5. Puzzle involving blocks (in AoL, there's no block-pushing, but there is a puzzle where you have to break blocks in a certain way)
AFAIK, those are the only things that appear in all the main Zelda games in some form. Rupees are close, but there are none in FS/FSA or AoL.