Many Jewish holidays seem to provide opportunities to give small tokens, especially to children. Are there any holidays, traditionally, which could especially provide reasonable justification for someone to give a gift, excluding major life events such as marriage, bar mitzvah, etc.
The seven days of Pesach, the eight of the holiday [Sukos and Sh'mini Atzeres], and other holidays are barred from eulogies and fasting. One must be happy and enjoy them with his children, wife, household, and tagalongs, as the verse says "be happy on your holiday". Although the happiness referred to there is that of the sh'lamim sacrificial offering…, also included is being happy — him, his children and his household, each with whatever is appropriate for him. How's that? Children — you give them roasted kernels and nuts. Wives — you buy them nice adornments and clothing, to the extent you can afford. Men — they eat meat and drink wine…. And when he eats and drinks, he must feed the transient[?], the orphan, and the widow, along with all the other paupers. One who locks up the entrance to his yard and eats with his children and wife but doesn't feed the poor and despondent — that's not mitzva happiness but the happiness of his belly.
There's a Jewish custom that fathers and relatives give children Chanuka money.
The poor youngsters have a custom of going from door to door [collecting] on Chanuka.
There's a custom to buy wheat to distribute to paupers for Pesach needs. Whoever lives in a city twelve months must donate to this.
The custom has spread that people allow children to grab the afikoman and hide it until it's time to eat it and don't return it until they assure them that they'll give them something. There are those who take issue with this, maintaining that one should not practice thus.
(All translations are my own and loose. And the sources I cite are not necessarily the earliest sources for what they say.)