For drinking cold, no. Never have. However, I use a Brita filter for all water that goes into the kettle or my espresso machine. Not for taste, but to remove the limescale/scum when the water is heated.
Don't like the idea of mineral water, as most has less minerals than my tap water. Plus, the environmental cost.
If I wasn't renting, I'd probably install a softener (bypassed for drinking water) so that washing/showering etc was better for my skin and required less soap. Had hard water when I lived in central London, and have somehow managed to find a rare place in Switzerland that is supplied with hard water too. Apparently, it's good for you.