Depending on the level and type of intelligence I try to pull out things players have never seen before such as novel uses for old spells or funky and unexpected combinations of spells or enemies.

I also avoid all the brute force and simplistic tactics that most enemies tend to employ (fighting on even terms, fighting to the death, direct contact, etc.) and strive to give the opponent advantage without railroading the players.

If opponents are superhuman or godlike in intelligence (I try to avoid using them altogether but when I do use them) I consider that regardless of the outcome some or all things will work out in their favor. For example, if BBEG wants to release a demon to wreck a city using an ancient tome that binds it then the party may try to steal that tome; only the act of stealing the tome from its safe releases the demon or at least begins the process (stolen or not BBEG wins). If they are that smart then no matter what happens they win until something they cannot outsmart occurs such as: brute force, sheer luck, fate/destiny/prophesy, an equal or greater counter-intelligence, etc.