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Tactical affairs such as movement and combat are best handled on a grid, but the grid need not be a bunch of squares. This variant replaces the squares with hexagons. (Hex grid paper and mats are available at many hobby stores.)
The primary advantage of this variant is that it eliminates the "every other square counts double" rule for diagonal movement, because it eleminates diagonal movement. Characters simply move from hex to adjacent hex, changing direction as they like. To determine the distance between two hexagons, just count hexes by the shortest path (in most cases, there will be a number of equally short paths).
Using a hex-based grid changes relatively little about the game, but it poses a mapping dilemma for the DM. Most buildings are based on 90-degree and 45-degree corners, so superimposing a hex-grid on a structure leaves the DM with many partial hexagons, not all of which are big enough for a Medium creature. Use this variant only if you're comfortable adjudicating these partial spaces on the fly.
Depending on their size, creatures may take up one or more hexagons on the grid.
Spell areas change to accomodate the hex grid.
Hexes and Facing
The hex-grid variant works well in conjunction with the facing variant, giving your d20 games more the feel of a tactical skirmish wargame.