David is correct. Here is a curl command that creates a test case result with a new line in the Notes field:
curl --header "zsessionid:_abc123" -H "Content-Type: application/json" -d"{\"TestCaseResult\":{\"Build\":\"1.0\",\"TestCase\":\"/testcase/1234\",\"Workspace\":\"/workspace/1111\",\"Verdict\":\"Pass\",\"Date\":\"2015-01-27\",\"Tester\":\"/user/777\",\"Notes\":\"line one <br /> line2\"}}" https://rally1.rallydev.com/slm/webservice/v2.0/testcaseresult/create