Yes, I can taste the difference between different brands of bottled water.
I don't swear I can tell them all apart, mind you. But I was drinking Sparklett's and then I started drinking Crystal Geyser and I decided I liked Crystal Geyser better. I also like it better than Dasani and Arrowhead and Aquafina and a number of other waters I tried. Some others — like Deer Park, which you don't find much in Southern California — are very close to Crystal Geyser. For the most part, I prefer water that comes from a spring to water that's been filtered, though I've encountered examples of each kind I didn't much like.
Even between good spring water and good filtered water, the difference is tiny. If I'm coming to your place to visit, please (pretty please) don't run out and buy Crystal Geyser just so you can be a good host. It's like the difference between an A+ and an A. One is perfectly fine. The other is, to a microscopic degree, perfectly finer. But whatever's on hand is usually okay.
And please…don't tell me the tap water at your house is perfectly fine. Once upon a time, the tap water at my house was perfectly fine and I wouldn't be buying bottles of the stuff if it was still perfectly fine. It's gotten worse and worse over the years. For a while, it was okay if I ran it through a Brita pitcher. Now, even that doesn't work. I had a city Water Inspector out a year or so ago and he ran tests and said it was perfectly safe, which I assume it still is, but even he couldn't stand (or explain) the taste. I decided it was better for my health to go with the bottled stuff, if only because I consume more water when I have the bottles available. Also, it's easier to drink if you don't have to hold your nose at the same time.