Is it a bad idea to keep a Macbook pro always on?

If you can, try to run the battery down every now and again. From Apple:

Apple does not recommend leaving your portable plugged in all the time. An ideal use would be a commuter who uses her notebook on the train, then plugs it in at the office to charge. This keeps the battery juices flowing. If on the other hand, you use a desktop computer at work, and save a notebook for infrequent travel, Apple recommends charging and discharging its battery at least once per month.

This debate very often pops up here. Long story short: Make sure you unplug it every once in a while (maybe weekly) and let it drain and charge. It is important to cycle the battery every once in a while for both the health and calibration of the battery. Check Apple's site for very specific Macbook battery tips here.

For proper maintenance of a lithium-based battery, it’s important to keep the electrons in it moving occasionally. Apple does not recommend leaving your portable plugged in all the time. An ideal use would be a commuter who uses her notebook on the train, then plugs it in at the office to charge. This keeps the battery juices flowing.

There are heat concerns - with the lid closed, there is less space for the heat to circulate. The hotter many computer parts are, the more likely they will have a shortened lifespan.

If you're worried about the battery dying, and don't ever need battery power, just remove the battery (if you have one of the newer ones), and see if the computer will remain on. Some power supplies have different circuits for charging and powering the laptop directly. Don't do this. Instead, do what others suggested and occasionally fully drain the battery (once every 2 weeks to 1 month should suffice).

I would also recommend you turn off your screen (just dim the brightness all the way) so you don't wear out (or burn in) your LCD.