小姐 xiǎojie - miss/young woman/prostitute (in northern China)
vs.小节 xiǎojié - (in music) one measure
小结 xiǎojié - summary
打算 dǎsuàn - plan/to plan
大蒜 dàsuàn - garlic
上海 Shànghǎi - Shanghai (the city)
伤害 shānghài - to injure
公里 gōnglǐ - kilometer
巩俐 gǒnglì - Gong Li (the actress)
眼睛 yǎnjīng - eyes
眼镜 yǎnjìng - eyeglasses
燕京 yànjīng - Yanjing (city name)
贵子 guìzi - precious (such as a child)
鬼子 guǐzi - devil (such as a child)
要是 yàoshì - if
钥匙 yàoshi - (door) key
杯子 bēizi - (drinking) glass
被子 bèizi - quilt
辈子 bèizi - a whole lifetime
病人 bìngrén - patient
兵人 bīngrén - soldier
You'll notice that this is not a problem in written Chinese because the characters for these words are completely different (though getting the thousands of different characters mixed up is another story). To my surprise I haven't seen too many funny or embarrassing misunderstandings, although being simply misunderstood is par for the course. Once a student asked me if the food her and her classmates had just gone through the trouble of cooking for me and Andrew was delicious and I said "no," to her surprise and her classmates' amusement. When she said xiāng (delicious) I heard xiǎng (would like) and thought she was asking if I wanted any more. I read a story about a foreigner asking for a banana (xiāngjiāo) cake in a supermarket and getting a bizarre look because he had accidentally asked for a rubber (xiàngjiāo) cake.
But one of the better stories I can remember about confusing tones came not from China but from a friend named Jenny in Thailand, where the language is also tonal. Whenever she referred to Thai boxing, known as muay thai, it would get a great reaction from the class. It's not always easy keeping the students' interest so she would refer to muay thai as often as possible in class, only to learn later that the way she was pronouncing it she was not talking about Thai boxing at all, but rather Thai pubic hair.
Any other stories/easily confused Chinese words out there?