Agra is in a sub-tropical place on the Indo-Ganges plains.
Thus, it has long and hot summer from the month of April to the end of July. At this time, the temperature can go as high as 45 degree Celsius (113 degree F). Loo is the name given to the wind that blows during summer. Loo is very dry and would agitate the summer.
If you want to get good deal on hotel bills and want to avoid crowd, summer is the right time. Make sure to pack some light cloths with you.
The monsoon usually starts at the end of July. But, some times, the monsoon would be delayed to the starting of August and ends by the end of September. During the monsoon season, the climate would be a little humid and the nights would be cold. The monsoon season would not be very wet and thus, you can also enjoy a rainy Agra if you wish.
Taj Mahal in rain would be a marvelling sight. From October, the temperature falls to 15 degrees Celsius (83 degree F). This is the time when tourists flock this land. Till February, this temperature would be maintained.
There is another reason for tourists flocking the place during February. A ten-day festival called Taj Mahotsav is celebrated in the month of February. During this a lot of fairs, cultural events and art galleries would be conducted.
There are lot of other festivals that marks the right time to visit the place like Holi, Diwali and others.