var header = GenerateAuthenticationHeader();
var userid = "5AB7EF25-BA14-E011-8EF1-001E902341EC";
var recordid = "BD3D383D-0317-E011-8EF1-001E902341EC";
var target = "TargetOwnedAccount";
var xml = "" +
"<?xml version=\"1.0\" encoding=\"utf-8\"?>" +
"<soap:Envelope xmlns:soap=\"http://schemas.xmlsoap.org/soap/envelope/\" xmlns:xsi=\"http://www.w3.org/2001/XMLSchema-instance\" xmlns:xsd=\"http://www.w3.org/2001/XMLSchema\">" +
header +
" <soap:Body>" +
" <Execute xmlns=\"http://schemas.microsoft.com/crm/2007/WebServices\">" +
" <Request xsi:type=\"AssignRequest\">" +
" <Target xsi:type=\""+ target +"\">" +
" <EntityId>"+ recordid +"</EntityId>" +
" </Target>" +
" <Assignee>" +
" <PrincipalId xmlns=\"http://schemas.microsoft.com/crm/2006/CoreTypes\">"+ userid +"</PrincipalId>" +
" <Type xmlns=\"http://schemas.microsoft.com/crm/2006/CoreTypes\">User</Type>" +
" </Assignee>" +
" </Request>" +
" </Execute>" +
" </soap:Body>" +
"</soap:Envelope>" +
"";
var xmlHttpRequest = new ActiveXObject("Msxml2.XMLHTTP");
xmlHttpRequest.Open("POST", "/mscrmservices/2007/CrmService.asmx", false);
xmlHttpRequest.setRequestHeader("SOAPAction", "http://schemas.microsoft.com/crm/2007/WebServices/Execute");
xmlHttpRequest.setRequestHeader("Content-Type", "text/xml; charset=utf-8");
xmlHttpRequest.setRequestHeader("Content-Length", xml.length);
xmlHttpRequest.send(xml);
var resultXml = xmlHttpRequest.responseXML;
Source: http://social.microsoft.com/Forums/en-US/a804bbe9-512c-44a9-b5b1-90f16b44a8b2/execute-method-assign-request-javascript?forum=crmdevelopment
