I'll assume that you've already bought the absolute essentials: a helmet, a lock, a pump, spare inner tube, puncture repair kit and allen keys to fit your bike (and I'd recommend a small seatpack to hold the repair tools so that you have them at all times).
helmet, a lock, a pump, spare inner, puncture repair outfit and allen keys
For rides of more than 40 minutes or so, then you'll need
a water bottle. The simplest and most common method, of course, is a water bottle with a cage that bolts onto the frame. Alternatively, many riders, particularly mountain bikers, like to use a
hydration pack. These are a bit easier to use off road but you do have to consider the weight of water on your back and sometimes they can be a problem to clean properly.
Cycle computers are really neat, cheap and useful. It's great to know your average speed and how far you've been on a ride.
If there's any chance of you riding at night, then you need
bike lights to be legal - and safe. Rear LED lights are bright, inexpensive, lightweight, unobtrusive and reliable. The only downside is that they'e not actually legal on their own. For the front, a simple battery lamp with a halogen bulb is great for short rides, but if you ride further, or off road in the dark, you may want to consider something stronger.
I think this is probably enough to put you on the Christmas card list from your local bike shop!
Cycle commuting is great way of staying fit, but you'll probably need to do this in all weathers, so do consider mudguards to keep you and your bike a bit more protected from road spray. Even if you only ride for fun, a Crud Guard attached under your mountain bike's down tube will help to keep dirt out of your face.
When you really want to get into 'performance cycling' then it's worth buying a
heart rate monitor to help check on your progress and regulate your riding. The shopping list could be a lot longer, but I think this is probably enough to put you on the Christmas card list from your local bike shop!