Water has to be cold, with lots of ice. Warm water makes my stomach upset, unless I’ve been mowing the yard, then “room temperature” is okay.
Coke has to be very, very cold and from a can, poured over lots of ice.
Tea, I can drink iced or warm. I like it sweetened either way.
Milk, cold, no ice. Same with orange juice. Other fruit juices though, as long as they’re cold, I’m okay without ice.
I don’t drink coffee or alcohol, so those don’t apply. No Clamato for me, either.
I’m in Viet Nam for Tet, and everybody here drinks beer with ice. It’s mostly Heineken, Tiger, or similar-tasting local brews though, so it’s not like the ice is hurting the flavor.
Water is normally the only thing I put ice in, and then only at a restaurant. Too much bother doing it at home.
Pop that comes in a bottle or can gets drunk straight from the container, and if I’m drinking it at home it’s usually at room temperature - I seldom bother with putting it in the fridge. If I’m ordering pop at a restaurant I always specify “no ice” because I get more pop that way. 
Booze from a restaurant may or may not have ice in it; I drink it whichever way it comes.
Coffee and tea are always hot, unless I decide to get one of those bottled coffee drinks at the store - those are normally kept in the cooler, but they don’t get ice added to them.
Yes, I had heard that. But I found it not to be true. At least I found it not to be true in France, Germany, Switzerland, Italy, Spain, Luxembourg, and Macedonia. I don’t remember drinking anything that was supposed to be cold in Ireland, Iceland, or England, because I was there in the winter. I guess it’s possible that all those people serving me drinks thought, “Oh, here’s an American, let’s give her ice,” because I had to ask for them without ice (as I prefer them)–everywhere.
I rarely use ice for anything, except for the occasional cocktail that demands it. I don’t need soda with ice, as it usually is plenty cold enough and, well, at home I just drink it at room temp, not even bothering to put it in the fridge. But most drinks served in the US at least are plenty cold enough for me that I don’t need any ice, and all it does is just water down my drink.
Ice dilutes beverages. Maybe that’s the point for strong flavoured drinks, but for me, if it’s already chilled, I don’t see any need for ice.
As far as cocktails go, ice is not only to chill a drink, but to keep it chilled longer. The more ice, the longer it stays cold and the longer before it starts to melt and dilute it. Plus, in the proper glassware, it makes it easier to free pour drinks. For your typical highball, in the proper glass, with a full glass of ice, the proper ratio it 1/3 booze to 2/3 mixer. Thus it easier to eyeball your highball without having to jigger anything. (yes, I prefer the inverse of that ratio personally)
Now to you people who think you get more to drink if you ask for less ice, here’s what happens. You STILL only get one shot of booze, and end up with more mixer. And with less ice, it melts and dilutes it quicker. Plus PLUS, with more drink to drink, it takes even longer to drink, thus even more melted ice, thus even more dilution.
Pro lush tip if you WANT the larger quantity of mixer, order the drink in a tall glass, but with still a full glass of ice.
Personally, I never drink anything with ice in it. Some things I drink pre-cooled, like beer and soda, but I have gone many, many years without any ice ever touching my lips. I wouldn’t refuse an offered drink with ice, I simply never choose ice. At the self-fill drink machines, I just fill my cup straight from the fountain, without ice.
I have no ice cubes in my fridge, nor an ice cube tray.