I was swapping a breaker inside my panel and noticed something that struck me as odd--the garbage disposal and dishwasher are both being served by a single cable that contains a pair of red/black hots (marked "14-3 w/ ground"). Whoever hooked it up in the first place had connected the two hots to two separate 20 amp breakers that were positioned opposite each other. Now, the wires are only 14 gauge, so 20 amps is too much to begin with. But even if the breakers were 15, would there be a risk of allowing more current than that since two breakers are involved, or would both trip together the moment 15 amps was exceeded? The breaker type (square D QO) can accept two wires; would it be better to connect both hots to a single (15 amp) breaker?
Edit: The cable terminates in an outlet where the dishwasher is connected with a NEMA L5-20 plug (I'm finding 14-gauge wire mixed with 20 amp stuff all over the place here. Sigh). A short length of 14-2 w/ ground runs from the outlet box to the switch that controls the disposal, and another 14-2 w/ ground runs from the switch to the disposal itself. The cord between the plug and the dishwasher is also 14-2 w/ ground.
This is called a multi-wire branch circuit (MWBC). There is no danger of overloading the neutral IF the two hots are on opposite legs of your 240V service. If the two sides have equal current, it will cancel out and the neutral will carry no current. The worst case for the neutral is if one circuit is carrying full current and the other is off.
Having said that, there is another problem in addition to the 14 gauge/20 amp you noted. Code requires that a MWBC be powered through a dual breaker or at least the two breakers be handle-tied. This way, if one breaker flips, the other will too so that the entire cable is dead.
It's known as a multi-wire branch circuit, and it's perfectly legit. The two ungrounded (hot) conductors terminate at breakers on opposite legs of the service, and share a grounded (neutral) conductor.
Since it's 14 AWG wire, you're correct that they should be 15 ampere breakers.
Do not connect both wires to the same single pole breaker.