I don't get that much of a kick outta imagining Conan versus other characters.
I quite like imagining Conan just interacting with other characters. Conan versus the Fellowship in a fight would be cool, but wouldn't it be even cooler seeing Conan as the 10th member of the Fellowship? Why have Conan vs Tarzan when Conan and Tarzan could team up, exchanging observations on civilization and savagery? What sort of scrapes would Conan get into in Buck Rogers' 25th Century? Sure, there can be a fight in those interactions, but half the fun of a fight is the circumstances leading up to them.
But any time I watch a movie that features some sort of concrete manifestation of unnatural evil (especially any kind of monster) I inevitably imagine how Conan would battle it.
I apparently can't NOT do this, as I've been half distracted from dozens of films down the years by picturing the Cimmerian wading through a cluster of Humanoids from the Deep armed with only a sturdy dirk, clinging to the back of The Host's dinosaur-beast while wailing on it's skull with a battle axe, and using the Black Dragons to set up an oversize ballista to take down the Cloverfield monster.
I tend to do this, except it's during dull legal dramas or period pieces.