my father's parents never gave us gifts for xmas - that day was reserved for church and eating.
gifts were given out for St. Nicholas Day (December 6 or the 19th on the Orthodox calendar). it's an older European traditions that is still followed, especially in countries were religion was suppressed for decades under communist rule. in Scandinavian countries, gifts are exchanged on St. Lucia's Day (December 13), again leaving xmas for church and feasting.
Hanukkah and Kwanzaa both have gift giving traditions over multiple days.