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Here's a quick guide I think might help out some players out there when it comes to gifts and NPCs.
To give a gift, select the NPC you want to give it to and choose inventory (I key), hold right click on the gift item and select the gift icon in the radial menu. If the NPC loves the gift, you will see a rating increase between +6 to +8. If the NPC likes the gift, you'll see about +3 rating increase. If they're indifferent, a +1 rating is given. Certain gifts are plot items and therefore will trigger a cutscene. Here is a list of gifts each NPC prefer:
Alister: Figurines and magic related items. Early on in the game you'll probably come across some sculptures and whatnot, give these to Alister. Plot gift is an amulet found in Red Cliff Castle.
Morrigan: Jewelry. Earrings, amulets, gold-encrusted lockets and whatnot. Plot gifts include a golden mirror and Flemeth's Grimoire.
Leliana: Symbols of Andrastate. Coming from the Chantry Leliana has a fondness for Andrastate related gifts. Plot gift is a flower (named after Andrastate).
Sten: Paintings. Don't even bother talking to the guy early on, you'll just piss him off. Sten likes paintings. If he likes you enough you'll get a quest to find his lost sword, a plot gift.
Zevran: Bars of rare metals. This Elf likes bars of gold, silver, and other misc. rarities. He also has a fetish for leather, and his plot gifts include a pair of Antivan leather gloves and boots.
Wynne: Scrolls and Texts. Wynne likes text scrolls and books. I am unsure if she actually have a plot related gift. If she does I have yet to come across it.
Dog: Honestly I don't see the point of giving your dog gifts, you can't actually make him hate the hero nor does having +100 rating give him any bonuses. However if you insist, toss a lamb or beef bone his way when you find some. It's not like you can sell those for coins anyway.
Allister and Zevran also accept alcohol. I think all the male characters do with the possible exception of Sten.
Furthermore, you get far more points if the character has brought up their plot item in conversation. At least Leliana does. Either that or she likes flowers from my mage much more than she liked them from my warrior.