Ice is a very important part of most cold drinks, however not all ice cubes are the same. First of all, good water makes good ice, so if you don't have good tasting water at home, use bottled water or filtered water when making ice. After all, if you wouldn't drink the water straight, then you probably shouldn't use it to make ice.
Some time ago, the ice cubes used in drinks were quite different, at that time old fashioned metal trays made cubes which in turn were frozen solid and took a longer time to melt. Nowadays, many ice cube trays and ice that comes from ice machines are designed to melt faster, however that also means they dilute drinks faster.
If you enjoy drinking a whiskey or scotch over ice, then ideally the ice shouldn't melt too quickly and dilute the drink. Instead, the ice should stay intact, keep the drink cold and just slowly melt. If you prefer this, then you want to pick larger ice for the job. When you choose ice disks, half cubes or quarter cubes, the ice will melt much quicker in a drink.
However sometimes, this is exactly what you want. When making sweet drinks such as mint juleps and fruit drinks, then cracked ice is often the best thing to be used. Cracked (or crushed) ice is also preferred when you're using a blender, as it otherwise can damage the blender, and you want the right amount of slushiness.
If you want to put high quality ice in your drinks, then you have to make sure to keep the temperature in your freezer cold enough. Also, if you're making ice for drinks, it can be fun to add a decorative touch to them by adding an edible flower, thin slice of lemon or a berry or two in the water of each ice cube tray before they freeze.