Well, that’s settled: The best way to have lots of good-tasting ice is to buy it by the bag. If you have the freezer space, keep a spare bag for iced drink emergencies. Keep the rest in a covered container, or in large ziplocs.
Making your own ice using filtered water (like Brita) may help the taste, but there’s always the risk of it picking up off flavors during the freezing process, from other items in the freezer.
Janet says an ice-making refrigerator is worth the money. Maytag has a model with a water filter in it that really makes a difference.
Board Links: Buying bags of ice