Na kartce pocztowej
Greetings / Best wishes from Capri.
[infml] Wish you were here!

All best wishes (from) Helen and Norman.
Urodzinowe
Many happy returns (of the day).
Happy Birthday.
All good / best wishes for your birthday.

Bożonarodzeniowe [i noworoczne]
Best wishes for a Merry / Happy Christmas and a Prosperous New Year.
lub
Merry Christmas and a Happy New Year.
Christmas / Season's Greetings.

Wielkanocne
Best wishes for a Happy Easter.
lub
Happy Easter

Z okazji ślubu
Every good wish to the happy couple / to the bride and bridegroom on their wedding day (and in the years to come).

Powodzenia na egzaminie
Every success in your (forthcoming) exams.
All good wishes for your A-levels / GCSEs.
Z okazji przeprowadzki
Every happiness in your new home.
W chorobie
Get well soon!
lub
All best wishes for a speedy recovery.

[infml] - nieformalnie