The only decent D&D games I've played threw out at least half the rules. But at that point wouldn't you be better off starting from a more rules-light system? On the whole I've had better experience with games in the World of Darkness family, and even better with those at a FATE-like simplicity level.
The rules most commonly thrown out around my table are things like "carefully track how much all your equipment weighs to make sure that picking up that loot won't make you encumbered", or "track the exact number of experience points you need to level up". Those aren't the most interesting bits of D&D, those are just the "if you really need a rule for it, here's one" bits.
I enjoy rules-light systems as well, for certain types of games that don't fit at all into a D&D-ish framework. But for anything that roughly fits the parameters of 5e, our group tends to gravitate towards 5e and enjoy the majority of its structure.
