Sure. On the sheet where you want the list to reside, give your list's range a defined range name. (Insert > Name > Define. Name it something like "MyValidationRange").
Then on the other sheet where your validation dropdown will reside, use
Data > Validation > List and for the source, enter =MyValidationRange (or whatever you really named the range).
Hope it helps.
EDIT:
We can come up with a number of ways to do this with vba, but the validation method is the way I would go.