I have taken overnight trains from Agra/Varanasi (in AC II) and like tranmerechris and AA25 quite enjoy rail travel in India. Will be taking these trains again when in India this Dec/Jan with my family.
I haven't taken the train from Mumbai to Agra but if time is of the essence flying from Mumbai to Delhi on one of the domestic airlines is a good choice.
I flew Air Deccan from Delhi to Mumbai, Mumbai to Goa and Goa to Delhi 2 years back and would recommend them as a good low cost carrier--they were reliable, nice aircraft with no frills--no assigned seating etc.
I would then hire a car and driver to go from Delhi to Agra, it's only a few hours(about 3-ish if I remember correctly), not expensive (less than a flight) and when all is said and done it would probably take less time that flying from Delhi to Agra as you don't have to deal with getting to from airports etc. etc.
The only bit about train travel in India I don't like is getting on and off the train. The trains don't stop long, about 3 minutes on the routes I've taken, and it is chaotic with people pushing and shoving to get on and off at the same time. Good to have your belongings ready and be near the door when you reach your stop.
Love AA25's advice on the tea. Just listen for vendors saying chair, chai, chai..
Hope you have a great trip while in India.