I rarely return to Andersen's fairy tales as an adult. My early exposure to Grimm's fairy tales came along with a nicely illustrated companion volume of Andersen's tales. And because I read whatever I could get my hands on, I read about the Girl Who Trod on a Loaf, and The Red Shoes. These stories in particular still frighten me. And I feel sorrow and pity when I read about the Little Mermaid, trying to do enough good deeds in 300 years as an insubstantial spirit to earn herself a soul.
Most Andersen fairy tales left me disturbed long after the story ended, unable to understand why the characters deserved the fates and punishments they encountered. Perhaps for this reason, I often enjoy retellings of Andersen tales as much as or more than I enjoy the originals. I love Andersen's Snow Queen, but delight in Patricia McKillip's version of the Snow Queen in the Datlow and Windling edited Snow White and Blood Red.
So I've got very mixed feelings about Andersen fairy tales. The language is lovely, and the images and characters stick in my mind, but the underlying morality of the fairy tale worlds Andersen creates often does not match well with mine.