a letter to your father would still be dear dad.
Kochany/ Kochana... (tato,mamo) or friend's name (depending on how close the relationship is)
Mój kochany/ Moja kochana/ Moi kochani
A letter to a friend and his wife.. Dear Max and Kate
Drogi/ Droga/ Drodzy....
witaj/cześć/dzień dobry? (is dzień dobry even a valid way of addressing someone in a letter/email etc??)
no name following those is necessary...
what about a formal letter, a job application for example.
usually "Szanowny Panie/ Szanowna Pani/ Szanowni Państwo"
can't think of any other way right now... :)