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A very popular train among the visitors to Agra coming from Delhi is the Shatabdi Express that connects New Delhi with Bhopal. This train passes via Agra. The added attraction is its schedule, making it a good option to visit Agra as a day trip from Delhi.The train leaves New Delhi by 6.15 am and reaches Agra Cantonment Station by 8.12 am. This is the fastest train to in this route (about 2 hours). Otherwise the regular travel time for an express train on the same route is 3 to 4 hours or even more.

Similarly, the fastest way to get back to Delhi from Agra after the Agra tour is also the Bhopal to New Delhi Shatabdi Express. Arriving from Bhopal ,this train leaves Agra Cantonment by 8.30 in the night and reaches New Delhi 10.30 pm.
The train Numbers for this train are :
New Delhi to Agra (Bhopal) : Train No 2002 (on Fridays it is Train No:2002A)
Agra (Bhopal) to New Delhi : Train No 2001 (on Fridays it is Train No:2001A)
Note the difference in the train numbers on Fridays. The train has a slight change in the schedule on Friday ( takes some 15 minutes longer), so a different train number. Also keep this in mind when book a ticket on Fridays.
While this is the fastest, and obviously not the cheapest train. It's about Rs450 ( about USD 10 ) for a chair car ticket.That includes the food served inside the train. Otherwise it's about Rs150 ( 3 USD) for a sleeper class ticket on a regular express train.

The next early morning alternative for Agra from Delhi are the Chhatisgarh Express ( Train No: 8238) leaves Delhi ( H Nizamuddin station) by 4.40am and reaches Agra Cantt by 8.30 am; Punjab Mail ( Train No:2138 ) leaves New Delhi by 5.25 am and reaches Agra by 8.50 am; Taj Express ( Train No: 2280) leaves Delhi ( H Nizamuddin station) by 7.10 am and reaches Agra Cantt by 10.07 am; and the relatively slower Udyan Abha ( UA ) Toofan Express ( Train number 3008) at 7.35 am at New Delhi (Agra by 12.10 pm ), though toofan means storm !

Then there are a plethora of weekly and by-weekly express trains leaving Delhi by 6'ish in the morning towards Agra. All takes bout 3-4 hours to reach Agra. Some of the examples are
H Nizamuddin to Mysore Swarna Jayanti Express (T. No: 2782 , Mondays);
H Nizamuddin to Ernakulam Millennium Express (T. No: 2646 , Tuesdays);
H Nizamuddin to Vishakapatnam Swarna Jayanti Express (T. No: 2804 , Wednesdays);
H Nizamuddin to Kolhapur Express (T. No: 2148 , Thursday) ;
H Nizamuddin to Trivandrum Central Swarna Jayanti Express (T. No: 2644 , Fridays);
H Nizamuddin to Kanyakumari Thirukkural Express (T. No: 2642 , Saturdays);
...and there are few more such trains.
For all those early morning trains get a sleeper ticket reserved. You'll catch up the lost wee hour's sleep to get to the railway station and also you'll arrive Agra in full energy, though feels a bit sleepy still!
So if a day trip of Agra is not your idea, there are a lot more trains to Agra from Delhi during the later parts of the day.

Mangala Lakshadweep Express ( Train No 2618 ), 09:20am from H Nizamuddin ; Jhelum Express ( Train no. 1078), 10.25am from New Delhi; Kerala Express ( T No 2626) , 11.30 am from New Delhi ; Kalinga Utkal Express (T No. 8478 ) , 12.05 pm from H Nizamuddin ; Amritsar Nanded Express (T no. 2716), 1.25 pm and so on.

The trains so far listed is not even half from the list of trains operate in this. As a thumb rule you'll find in every hour some 2 or three trains from Delhi to Agra. Some leaves from NewDelhi while the rest from H Nizamuddin.

The same is true for the return journey (or onward journey from Agra ) too.
By the way , apart from the main station Agra Cantonment, most the trains stops at Raja ki Mandi railway station too. Some of them (Toofan Express) even gets you to Agra Fort railway station, located just around the corner of Agra Fort and also closer to Taj Mahal. So get an idea of the stops at Agra too for the train in which you've booked. You can save a bit of time in cutting through the Agra's city traffic. If you are not very sure of all these, Agra Cantonment is the station for you.

Please check with the Indian railways website for the updated schedules, as there could be changes in the due course.