I guess my luxuries come in stages, and "never" is an awfully hard line to draw.
Stage 1: I would very much pref not to give up running water, but it can be done without (I've not lived without it for any real extended period, but my father grew up without it). So I can't say "never," and I know it's a luxury, but I'd give up many other things in order to keep it. Especially potable running water!
Stage 2: refrigeration. This I have lived without for an extended period (about a month), and the task of feeding a family is much more difficult.
Stage 3: Running water that comes in hot and cold. I do like this, very much, especially for bathing. But I have been living without it in my kitchen for almost a year now-- it's not essential. Still I'd gladly replace the water heater if it died.
Stage 4: Electricity (not listed before refrigeration because propane refrigerators). Lights, heat, AC, and computers are nice. Again, though, I know it's a luxury because members of my family grew up without it, though I did not.
Stage 5: Home Internet and wifi. Definitely have lived without it since I'm considerably older than the Internet, but I like it, very much.
If I have a choice, I'll try to keep all of theses stages of luxury in my life, and if forced to drop any, it would be in reverse order from Stage 5 to Stage 1. But I can't say I'd "never" give up any of them. The things I can never give up fall firmly into the lower levels of Maslov's hierarchy of needs, and these don't, modern conventional wisdom notwithstanding.