Starting with Hagrid's gift to Harry of Hedwig, with Harry's objection that Hagrid doesn't have to buy him a gift, and Hagrid's easy response that he knows he doesn't have too. Giving socks to Dobby. Sirius's giving Ron an owl because it was his fault he had lost his rat. Some of course are heavily plot signficant, like Dumbledore's bequests to the trio. Others are heavily characterization -- Sirius gave Harry a broomstick twice, not just in Prisoner, but for his first birthday as well. Mrs. Weasley gives him clothes and food, classically maternal gifts.
Oddly enough, the one that I found most moving was the watch that Mr. and Mrs. Weasley gave him for his seventeenth birthday, having just brought up the custom, and Mrs. Weasley's explanation that it had been her dead brother's. If you've read with care -- or perhaps read off-line stuff about it -- you know that Fabian Prewett and his brother Gideon were killed by Death Eaters, five of them attacking at once, and the brothers fighting like heroes, as Mad-Eye put it. The odd thing about this is that it's completely insignificant to the plot. At the very end, in the epilogue, Harry checks his watch, and it's mentioned that he cherished it, but he does not need it for the story. Still it stuck in my memory.
One wonders if this kind of motif can be planned. . . in my experience, they creep up on you, but then you may notice them in time to realize you need to lard in more instances to spread it around more evenly.