Yes, you can reheat coffee but the whole taste will usually change. It is not recommended, as it is just as easy to make a new cup of coffee or tea. If in a retail situation where you have customers buying coffee or tea, never reheat. Some machines such as percolators and drip filters are designed to keep coffee and tea warm, but not to be reheated and used for resale. You may also find that there are Government regulations regarding this issue and therefore you should seek further advice.
On a personal/private basis however, if you wish to reheat coffee your best option would be to drink it as a Caffé Latte, where you are using the coffee as a flavouring agent rather than a major ingredient. Here you can mix the coffee and milk together in a pot when heating.
Another way to re-use/reheat coffee or tea is when using it as iced coffee or iced tea, particularly in summer. See "The Zone" for recipes on iced coffee, iced tea and Caffé Latte.
Overall it is not recommended to reheat either coffee or tea, as this will extract bitterness, make it lose the wonderful aroma and have a different flavour. It is Ok to re-use coffee/tea to make one of the above drinks for personal consumption, however keep in mind that like any food/drink they can go off if not kept properly.