being that you can get thousands of miles of use out of a standard rim brake setup and a well set up rim brake still performs exceptionally well, you don't neeeeed disc brakes. but upgrade-itis can be powerful. since everyone has outlined all the benefits, i'll just add a list of cons that i've had to deal with from experience on the mtb side.
- brake squeal - when you get oil on your rotors or pads you'll get a high pitched squeal any time you brake. for this reason, you should keep things clean with alcohol after every few rides. even oils from your sweat can contaminate. it's easier to clean oil off of rotors and harder to clean oil off your pads. brake squeal is also more common with higher metallic pads. brake performance is minimally affected, but the sound can get annoying.
- rotor true - probably less likely on road riding as there aren't risks of bashing your rotor against rocks or roots or crashes, but your rotors are subject to getting bent and then have to be bent back into shape. this will affect braking performance.
- bad bleeds - if you get air, foreign materials or water trapped in your hose line from a bad bleed, your braking performance will go to ****. cleaning a compromised line is a headache, but completely necessary if this happens.
- pad lock - if you take your wheel off for any long period of time (storage etc.) you need to remember to shim your pads or else they will lock closed and you'll spend an hour cussing as you work to reset your pads before your next ride.
that all being said, i love disc brakes. i've had and maintained disc brakes on my mountain bikes for a decade. the braking performance is just so much better, even given all the hassles mentioned. all my road bikes are rim brakes but if ever i purchase a new road bike it will be disc compatible. part of this is also because i see the industry phasing out rim brakes in the future.