Depends on the actual drivetrain, but if you have anything nice on there, you’ll likely have to replace the following:
Front Derailleur (dont have to, but this is the cheapest of everything, and will work better with a double)
Rear Derailleur (need a shorter cage)
Crank (obvious)
Bottom bracket (only if Octalink or Isis and the such, you’ll need a shorter spindle)
Left (front) Shifter (if Dura Ace; I believe Ultegra and lower work for both double and triple)
What components are on the bike currently?
As Kerving stated, you might be able to change only the crank (triple to a double) BUT when you start changing drivetrain components you might find that need to change everything because of wear. With a double you can run a shorter chain if you switch to a short cage rear derailleur. If you change the chain you might end up having to change the cassette as well and considering there will be new front chainrings you may as well start fresh and add a cassette and chain to the list then you know where you stand.
Tell us more about your current components on your bike make / model?
For example: if you have older ultegra the STI levers and be used for double and triple application, I have found the long arm deraillur and front derailur work fine with a double crank.
Same thing I was thinking - wont make the weight weenies happy but a long cage will work just fine with a double.
Chip,
That’s true. The throw might be a bit more but you may actually have less rubbing issues with the triple crank front derailleur. The tolerances with the 10 speed drives can be pretty narrow - ie 1mm one way or the other.