Turning someone to stone just by looking at 'em is a rare gift indeed. So rare that, prior to the advent of Dungeons & Dragons, I know of only one creature in mythology or folklore that had petrification as a natural ability: the three gorgon sisters, of which Medusa was one.
No, basilisks do not turn people to stone, unless you mean in the Old English sense of "dead as stones." The cockatrice doesn't either, despite its Wikipedia entry (it cites page 186 of a poorly reviewed eBook fantasy novel as its "source" for this ability). The "gorgon" bull-creature was derived from a misnamed account of the catoblepas, and given its stoning power by Gygax (as actual folkloric depictions of the the catoblepas simply has a "death gaze" like basilisks).
|"I'm practically a demigod!"|
There are depictions in fantasy and folklore of magicians turning folks to stone, and I'll be happy to address that in the spell section of this series (coming up!). But monsters turning people to stone is something that doesn't need to be modeled...and thus no saving throw is necessary.
Now, if you really, really, REALLY must have gorgons (like Medusa) in your fantasy game, I understand it. But you still don't need the saving throw. What would such a save represent? The hero saying, "Must...not...turn...to...stone!" And they get so much better at it as they go up in level?
That's how D&D 3.5 (and presumably Pathfinder) represented it...as a Fortitude save. "My 7th level fighter is resisting her petrifying visage?" What? How? "By being extra tough...he has control over the very molecular structure of his body and he's saying, 'Don't calcify, cells!'" Certainly Perseus (a high level fighter and Zeus's son) could have stared her down if such was the case.
No, clearly this is one of those examples of: if you're going to bother to put it in the game, then let it work. The PLAYERS are going to need to come up with ideas/alternatives for beating such a creature...as did Perseus...something besides, "well, I'll just tough it out with a saving throw." You're going to have to fight blindfolded, or use a mirror...either with a substantial penalty to your attack roll. Or else, try to sneak up on the thing when its sleeping (hoping that it's back is turned to you). Depending on the tactic used, the penalty might be more or less (though possibly with a percentage chance of accidentally catching a peek of the creature when embroiled in melee).
Creatures that have these types of auto-kill attack...because that's what they essentially are (you need a 6th level spell to bring 'em 'back to life,' as opposed to the 5th level raise dead, but even so)...should only enter into a campaign setting with some pretty substantial clues to tip off characters' cleverness. How was a basilisk's "death gaze" defeated in mythology? By carefully placing mirrors about the creature's lair while it was sleeping. But its body is deadly poison as well...best handle it only with thick gauntlets.
If the banshee's wail causes death, best stuff your ears with cotton (or strips ripped from your tunic).
These are the kinds of tricks players routinely come up with. Good DMs don't let the rules get in the way of a good player idea...but then not every DM is "good," and not every player is inclined towards thinking "outside the box." Don't give 'em an excuse not to: get rid of this saving throw and let the chips fall where they may.
[oh, just a quick side note: I see at least one reader thinks these posts are "shite," based on the box he/she checked. However, I don't really see any negative views expressed in the comments section. Not trying to call you out, pal, but I would certainly welcome your dissenting opinion...just an FYI. Being told I'm wrong and why doesn't bother me all that much. Sometimes it even changes my mind]