Can a dishwasher and disposal share a dedicated 20 amp circuit?

Original answer: Yes! I did this in my Kitchen

USSEG: It really comes down to how much amp each of the appliances is going to use at peak. You need to look at the emperage draw of each appliance then make your decision. If you are sure you are not going to use both at the same time (ever) then it is fine. A disposal requires at least a 15 amp and a dishwasher usually needs at least a 15 amp.

If breakers start tripping you will need to separate them.

If this is for new contrstruction, there is no reason not to run a separate line for each.