The range of players varies according to the range adder of the weapon equipped and the size of the monster being attacked. 
Range = range adder + size
Players achieve maximum range by equipping range adder 4 polearms and spears, giving them range 5 when attacking size 1 monsters, range 6 when attacking size 2 monsters and range 7 when attacking size 3 monsters.
Although the physical damage of Smite and Dragon Talon, Dragon Tail or Dragon Flight is based on shield and boot damage respectively, range is still based on the range adder of the weapon equipped.
When an Assassin or a Barbarian equips two weapons and attacks a selected target, range is based on the range adder of the primary weapon (the weapon equipped above the gloves in the inventory, or that first equipped). The primary weapon is displayed in the right hand of the Assassin or Barbarian. This is true for Dragon Claw and Double Swing and Frenzy, even though these are a sequence of two attacks (as are Normal Attack and Fists of Fire, Claws of Thunder and Blades of Ice when used with two weapons). While each weapon attacks and applies its damage and modifiers individually, the range applied to both attacks is still that of the primary weapon. 
Both Burning Dead
(size 2) are out of range when a Dirk
(range adder 0) with 100% Chance to Cast Frost Nova
is primary and a Long Sword
(range adder 1) with 100% Chance to Cast Nova
on Attack is secondary. When the Long Sword is primary both
attack the Burning Dead (which are chilled by the Frost Nova cast by the Dirk).
Mercenary and pet
The range of all mercenaries and pets varies according to their entry in the MeleeRng column of MonStats2.txt and the size of the monster being attacked. 
Range = MeleeRng + size
Equipping weapons has no effect on the melee range of mercenaries and pets that can do so e.g. the range of a Desert Mercenary or Valkyrie equipping a War Pike (rangeadder 4) will still be based on MeleeRng 2 and 0 respectively.
The range of monsters varies according to their own entries in both the MeleeRng and SizeX/Y columns of MonStats2.txt. 
Range = MeleeRng + size
Players, mercenaries and pets are all size 2. Regardless of size, the target is always the central occupied sub-tile. 
When a monster is blinded by Hit Blinds Target, Dim Vision or Cloak of Shadows, its awareness range is reduced to its melee range; thus it's relevant even if they are ranged or casters with no mêlée attack.
The only size 1 monster that has a melee attack or that can be blinded is a Flying Scimitar which has MeleeRng 2, giving it range 3 (2+1).
- Tentacle Beasts (River Stalkers, Water and Stygian Watchers) of Act 3 have MeleeRng 6, giving them Range 9.