My post about weapon damage yesterday earned a mild and entirely justified rebuke from Brendan of Necropraxis, who pointed out that even a straight 1d6 weapon damage system doesn't necessarily make weapon choice purely an issue of style. While I do prefer my combat stats just a wee bit crunchier than straight 1d6, I found his point that weapons can be distinguished by other factors, both in and out of combat, worthy of a follow-up post. What's more, these factors need not be codified in stats - in fact, an intuitive approach may be best. (Trying to stat up every function of a weapon draws one into the trap of thinking that it can't do anything but what the rules explicitly say it can do, a trap that I have to admit I fell into a bit. Sometimes less airtight rules encourage a broader view of things.)
First, there are differences in how various weapon types might affect the physical forms of different monsters. In B/X, there's no rule that says skeletons take less damage from slashing or piercing weapons than from bludgeons, but it makes a great deal of sense. There's a lot of empty space between those bones, and no flesh to slash with a blade. A sword might do some impact damage, but it seems intuitively obvious that you won't do it much harm with a dagger or an arrow or a spear-thrust. Breaking those bones with a stout blunt instrument seems like the best bet. But hey, maybe the player wants to use the haft of her spear like a quarterstaff? Why not? It makes perfect intuitive sense, without needing to be hard-coded into the rules.
What happens if you smack the resilient substance of a gelatinous cube with a club? What about when the finely-honed edge of a sword meets the unyielding surface of a stone golem? Our basic understanding of how the physical world works suggests that the sword is better for carving up a living Jell-o mold, and a blunt weapon is better for beating a golem to rubble.
You don't need a bunch of new stats for each weapon, or each monster, just a blanket declaration that weapons that seem completely unsuited to harming a particular creature do half damage, or 1 point, or whatever, and apply it whenever common sense tells you that it's applicable.
Then there are the non-combat uses of weapons. If you want to emphasize exploration over combat, it makes all the sense in the world to play up the differences between weapons as tools. You can drive iron spikes with a war hammer in a pinch, or perhaps with the back side of your battle axe, if it doesn't have another blade or a spike there. You want to pry the gemstones out of that throne? I hope you have a dagger handy, because your fingers aren't going to do the job. Forgot your ten-foot pole? No problem, if somebody's got a spear, staff, or polearm to hand. Heavy wooden door blocking your way? Better have an axe, because you're not going to do more than mess up its finish with a sword or club. The odd little hooks and flanges on many polearms make them great for retrieving items out of arm's reach. And so on, to the limits of player imagination...
In short, if a character tries to do something that experience or common sense suggests requires a tool, the DM is perfectly justified in asking what he's using to accomplish the task, and quite often a weapon makes an admirable stand-in for a common tool. It's up to the players to think outside the box, of course, but it's up to the DM to encourage that by rewarding them with success when their idea makes good sense, whether the rules expressly endorse it or not.