Some games use a hexagonal grid, which is better though not perfect. A hexagonal grid is probably the best approximation to Euclidean geometry that you can get with a simple regular network.
It occurs to me (and has without doubt occured to others, but hey) that a somewhat random grid could be made to approximate Euclidean geometry arbitrarily well, at least over long distances.
Could be useful for loop quantum gravity and all that (again, this is no-doubt well known to physicists, but it's new to me and this is my blog). Reality could be a network of this type, and Euclidean geometry the approximation (or rather Einsteinian continuous not-quite-Euclidean geometry).