The Dragon Age Wikia has a ton of information about this with a complete list of all the items you can give to each character. I will paste the summaries for each character here:
Alistair
Alistair has a preference for strange runestones and figural studies of arcane creatures (excluding Totem, which is preferred by Sten).
Dog
Dog has a preference for foods and bones, but his approval rating will always be 100% so you can boost one of your other companions' ratings with gifts originally meant for Dog.
Leliana
Leliana has a preference for holy symbols of Andraste, as well as shoes.
Morrigan
Morrigan has a preference for jewelry such as necklaces and pendants.
Oghren
Oghren has a preference for alcoholic beverages (excluding Wine, which is preferred by Wynne).
Shale
Shale has a preference for the nine "remarkable" gemstones that can be found in Ferelden.
Sten
Due to an aspect of Qunari discipline, Sten has a preference for paintings.
Wynne
Wynne has a preference for books and scrolls.
Zevran
Zevran has a preference for leather items and bars of precious metals.
Secret Companion
The Secret Companion has a preference for maps of Thedas.