According to the rules of American Standard English (the most correct form of English in the world today) when referring to two or more people, “their bodies” is always correct. “Their body” actually means two or more people share the very same body. So, if you’re referring to conjoined twins, for example, who have two heads but share one body between them (who usually have actually two partial bodies joined at the spine joined to one pelvis and one pair of legs) it would be correct to say “their body”; but in every other case, where each person has his or her own body—no matter how similar—the correct wording is “their bodies.” There are NO exceptions to this rule.
NOTE: Using the word “their” to mean his or her, when one’s gender is unknown, is linguistically incorrect—always. If one’s gender is unknown, the correct word is “he” (or him). For example:
Incorrect: “Someone called while you were out.”
“What did they want?”
“They said they would call back later.”
Correct: “Someone called while you were out.”
“What did he want?”
“She said she would call back later.”
This may be politically incorrect, but it is linguistically correct.