Personally, I pronounce "z" as zee, so does my family. I've never actually heard it pronounced "zed".
Ay Bee Sea Dee Eee Eff Gee Haytch Eye Jay Kay El Em En Oh Pee Que Arr Es Tee You Vee Double U Ecks Why and ZED
We're pretty weird. There is a convention here on when to use "zee" or "zey". Yes, we say "zee" or "zey". When z is preceded or succeeded by any letter that would confuse z with c, we say "zey". If you can't say the buzz which, unfortunately, plagues our population), "sey" means z. If both conditions are not present, you can safely say "zee". In the alphabet song, all three pronunciations (zee, zed, zey) are okay to use. When someone says "zeta", they're automatically Spanish descendants.
Ay, Bee, Sea, Dee, Eee, Eff, Gee, Heytch, Eye, Jay, Kay, El, Em, En, Oh, Pee, Que, Arr, Es, Tee, You, Vee, Dubleya, Ex, Why and ZED,
Ay, Bee, See, Dee, Eee, Eff, Gee, Eych, Eye, Jay, Kay, El, Em, En, Oh, Pee, Queue, Arr, Ess, Tee, You, Vee, Double You, Ex, Why and Zee!
Zed. Americans tend to pronounce it like "zee" because it rhymes with "vee" in the alphabet song, but that's just lazy. Pronounce it properly. Z-E-D.
Zee Aye, Bee, See, Dee, Eee, Eff, Gee, Aytch, Eye, Jay, Kay, El, Em, En, Oh, Pee, Que, Arr, Ess, Tee, You, Vee, Double-You, Ecks, Why, and ZEEEEEEE