I have a mobile phone that gets a lot of calls directly, but I wanted to log those calls to a CRM.

This is a partial solution.. Android Notifier (http://code.google.com/p/android-notifier/) is an app that can be installed on the android and send a UDP message to a server (or also to a desktop client) when calls come in. The desktop client can launch a website to pull data for a screen pop of some sort....

It seemed to sometimes lose sync (when wifi went off and then came back..) but it's got the last 10 messages or so.

I have it send to UDP, and this small node.js script saves the time-stamped messages to a file. (Note: timestamp is in milliseconds..)

//http://code.google.com/p/android-notifier/wiki/NotificationProtocol
//DEVICE_ID/NOTIFICATION_ID/EVENT_TYPE/EVENT_CONTENTS
var fs = require('fs');
var log = fs.createWriteStream("incoming_call_log.txt", {'flags': 'a'} );
var dgram = require("dgram");
var server = dgram.createSocket("udp4");
server.on("message", function (msg, rinfo) {
//  console.log("server got: " + msg + " from " +  rinfo.address + ":" + rinfo.port);
//  console.log("Got: " + Date.now() + "/" + rinfo.address +"/" + rinfo.port + "/" + msg);
              log.write(Date.now() + "/" + rinfo.address +"/" + rinfo.port + "/" + msg +  "\n");
});
server.on("listening", function () {
  var address = server.address();
  console.log("server listening " +   address.address + ":" + address.port);
});
server.bind(10600, "YOUR IP");