Most Greeks do not celebrate their birthdays, instead they have what is known as a name day (Yiorti). You may hear the expression “Yiortazo Simehra” which is the equivalent of it's my birthday today.
Children are normally named after a saint and celebrate their name day on the day devoted to that saint in the religious calendar. This means it is difficult to forget birthdays as so many people celebrate on the same day. For example, the 21st May is the day sacred to Saints Konstantinos and Eleni. This means that every man with the name Konstantinos (Kostas), and every woman called Eleni will be celebrating their name day.
The appropriate wish is “Kronia Polla” (many years). If you have a friend celebrating a name day, it is customary to drop in to say 'Kronia Polla' and take a token gift. This may be something like flowers, sweet cakes, or even a bottle of spirits. With more elderly friends, you can reinforce 'Kronia Polla' by saying 'Na Ta Katostisete'(may you live to be a hundred).