I can honestly say I own every Zelda game, just not all for their original systems. I even own multiple copies of some Zelda games, such as TLoZ on both Collectors Edition and Classic NES series and OoT on both Collectors Edition and the GCN Master Quest re-release. I have ALttP on GBA (Four Swords re-release), both original carts of the Oracle series for GBC, Link's Awakening DX re-release for GBC, Zelda II on Collectors Edition and Console Classix emulator, and all other Zelda games for their original systems (except Majora's Mask on Collectors Edition).
No, I don't have the CDi games. Those don't count. It's not difficult to find LoZ titles. Nintendo re-releases them so frequently there's always some version readily available (Oracle games are an exception) unless you really want one of the older games for its original system.