As with most major cities, there are peak times of travel on the tube that you really should try to avoid. These times are when the London commuter squashes their way into the last minuscule space on the train and spends a journey with their nose pressed into another commuter's armpit. So really, it's not to be recommended.
The morning 'rush hour' hots up between about 7:30 am and 9:30 am and the evening peak time is between 4:40 pm and 6:30 pm.
If you find you need to travel between these times, try and find a bus route so you can watch the commuters run around and not have to get caught up in the furor.
The tube can get busy and feel rather claustrophobic at other times of the day, but the pace should be a bit calmer than at peak times.