There is a limit to attacks per second in Warcraft III. I recall it being around 45 or something like that (likely 1 per internal frame).
To achieve this attack speed one must lower the unit's attack animation back swing value to near 0 and set its attack period to a small value. Attack animation back swing determines the wind up time for attacks and hence applies a minimum attack period limit.
There is a limit on faster attack speed from +400% to -80%. This is from all sources so includes agility, items and buffs which all stack additively. Values out of that range are clamped, hence a unit with an attack period of 1 can fire at most 5 shots per second by raising attack speed in game.
StarCraft II has a totally different set of limits. Attacks are limited to once per frame (16 attacks per game second maximum) and by default there is no limit on faster attack speed (one can be applied though by altering the attack ability).