In most games we sometimes come across a boss who's too much of a wimp to fight on his own. They summon a pack of mini bosses/goons to aid them in the fight. What's your usual point of strategy? Aim straight for the boss or take out all of the henchmen first?

Shoot the boss while sidestep + rotation dodge the henchmen attacks.

Depends on the strength of the henchmen.

If they're weaklings that wont really affect me while I'm fighting the boss I'd probably go after the boss. If they're something that will affect me and possibly screw me up I'll go after them first.

In that situation, I sometimes clear the henchmen first, since they'll be out of my hair quickly; Unless they respawn, then I can't be bothered.
There are a shitload of variables to this scenario to discuss.

For me, if the henchmen die when the boss dies, in that case I would have my fun with them before I knock off the big one (like doing these expensive special moves etc.). Except the boss almost kills me with one hit, then I take the boss first plus the henchmen which are stepping in my way.

Lavos Core was so cruel with his henchmen, damnit. I still haven't beat that mob.

Chrono Trigger of course.

Those aren't really henchmen, just three elements of Lavos. One dude (err... giant spiky world-destroying thingy), three parts.

Project Snowblind (old game, yes)--the general dude. He sends in spiders and bots, and in this case, I would say just shoot the henchmen first.
But, with all the types of games out there, there are probably as many FAQs and walkthroughs that tell you the best way to handle it.

Henchman first, even more so if your playing on the highest difficulty.
Otherwise they will be to much of a pain in the ass and kill you before you can even touch the boss.

And unless I'm mistaken, don't they make games where you can actually use the henchmen to defeat the boss himself?