Well, certainly! I play games that variously use 10-foot squares, one-yard hexes, one-metre hexes, two-metre hexes, that don't use any grids, and that don't use distance at all. Real distance matters in miniatures wargaming and in RPGs that are based on it, including original D&D, AD&D, BD&D, OD&D, and D&D Expert: D&D didn't use a grid until 3rd edition. And there are lots of others that don't use a grid at all. RuneQuest and the BRP family, I think; White Wolf's Storyteller family of games; lots of others.
There are also games that use grids to regulate movement and adjacency for the purposes of hand-to-hand combat, but use real distance for weapons range—such as James Bond 007 with its 10-foot squares. In several hex-gridded games such as GURPS and ForeSight/HindSight movement is explicitly regulated by the grid, but missile weapons are given ranges in yards and metres respectively, and grid distance is used instead of real distance only by convention.