This is an FX question. I want to track short term (overnight or next best thing) rates for major/em ccys. What's the best way of doing this? Is there an index I can follow? Preferably something published for free somewhere. :)
Look for the Overnight LIBOR or OIS rates for each currency. It's easier to find LIBOR rates by the way, but OIS are closer to being risk-free. In a nutshell, LIBOR rates contain bank related credit risk which may induce bias your analysis.
Also available for the USD is the fed funds rate and the ECB refinancing rate for the EUR.