The Delhi division of Indian Railways maintains a one-page website that offers the current status of trains arriving or departing from the Old Delhi, New Delhi and Hazrat Nizamuddin railways stations.
The charts update automatically and is an attempt to bring the live on-station charts online.
This nameless website, hosted at 18.104.22.168, is slow and not pretty but it offers one bit of information that you can otherwise get only after calling the railway station - it tells you the exact platform number on which your train will arrive (or depart from).
You know the kind of panic and chaos that happens when the platform number of a train is changed at the last moment (not an infrequent phenomenon) and the live information available on this little website will hopefully help you plan a little better.
Unfortunately, the site only has information for trains arriving in or out of Delhi.
Thank you Shantanu Chauhan for the tip.