Formal:
* Collection of postcards
* Set of postcards
Informal:
* Pile of postcards
* Stack of postcards
* Bunch of postcards
* Pack of postcards
More creative:
* Album of postcards (if they are in an album)
* Gallery of postcards (if they are displayed)
* Treasury of postcards (if they are valuable)
Ultimately, the best collective noun to use will depend on the specific situation.