Before we get too far into this, the Buddhist concept of mudita, "sympathetic joy" or "happiness in another's good fortune," is sometimes suggested as the opposite of schadenfreude.
While trolling around on wikipedia, there were several interesting suggestions for the equivalents of schadenfreude in several Asian languages:
For Thai, it's suggested the phrase สมน้ำหน้า, som nam na, would apply, and would be interpreted as: "You got what you deserved"; "Serves you right"; or "I'm laughing at your bad luck". I'm sure Lao and Hmong both have a parallel phrase, but I really wouldn't be able to tell you what it is right now.
In Korean, the phrase 고소하다, go so ha da, translates to "to smell sesame oil". It's an elaborate idiom: The phrase apparently applies because in Korea the smell of sesame oil is regarded as very pleasant, and this phrase is used when one is pleased about a particular event. It is especially used when one is pleased about "an event involving the misfortune of another," according to the Wikipedia.
For Chinese, the phrase xìngzāi lèhuò (Simplified Chinese: 幸灾乐祸; Traditional Chinese: 幸災樂禍) is apparently a classic idiom that directly translates to "enjoying (other's) calamity (and) laughing at (other's) misfortune". Very precise.
For Japanese, the phrase 他人の不幸は蜜の味, tanin no fukou wa mitsu no aji, translates as "others' misfortunes are the taste of honey". Mmmmm. Honey.
For Tagalog, it's suggested the phrase "Buti ngà sa iyó," fits. It's supposed to mean "Good for you", but can be translated as "Serves you right" or "Buti ngà sa kanyá" as "Serves him/her right." Apparently the short form is usually just "Buti ngà!"
In light of the Simpsons Movie coming out tonight, let's not forget the classic exchange between Lisa and Homer:
"Dad, do you know what Schadenfreude is?"
"No, I do not know what Schadenfreude is. Please tell me because I'm dying to know."
"It's a German word for shameful joy, taking pleasure in the suffering of others."
"Oh, come on, Lisa. I'm just glad to see [Flanders] fall flat on his butt! He's usually all happy and comfortable, and surrounded by loved ones, and it makes me feel...what's the opposite of that shameful joy thing of yours?"
"Boy, those Germans have a word for everything."