Always use pistols/melee in FPS games until it becomes impossible not to (examples - Halo, Fallout 3). Even if this means setting the game to the lowest difficulty, you will not find me with anything bigger than a pistol/fist. If it's possible to avoid guns altogether, I will, as in Mirror's Edge (I have never shot a single soul in my 2 1/2 playthroughs).
I often delete my save files on fighting games so I can unlock all the characters again (just for random fun, I don't get mad when a game comes with all characters unlocked).
If there is a power:growth tradeoff in an RPG, I will always go for growth, even when it makes the game difficult. For example, in Final Fantasy VII you get some weapons and armor early on in the game that speed up the growth of your magic. This seems like a pretty legitimate play style, but the quirky bit is that I will NEVER use the magic that I spent all that time leveling up.
Also in RPGs, I will never spend more than 2% of my total gold. So if I have 100,000 gold, I will spend maybe 1,000-2,000 on potions or something, but rarely ever more. Then I will spend it all on garbage just before the final boss.
ALSO in RPGs, if there are permanent stat boosters (like Rare Candy in Pokemon), or super rare items you can't buy (Elixirs in FF) I won't use a single one until the final final final battle. And this seems like total common sense to me, because stat boosts seem pointless at lower levels when you level up all the time, as opposed to later in the game you'll have a harder time gaining stats (and more likely you'll understand how to distribute them better). Also most battles aren't so difficult that you need to use expensive healing items, so why bother.
In many JRPGs, I simply won't use items period. Like if an item gives my characters some new super power (TMs in Pokemon, or the manuals in Inazuma Eleven), I'll never feel like I have a proper development plan, and the item will just rot in my inventory for the rest of the game. This is largely why I like the SaGa series, they force you to run through new equipment and items all the time.