I never had that problem with phoenix downs or potions as long as they can be bought in the shop, since they're always so cheap after the beginning. Elixirs and other technically-limited items, however, only get used once I get really frustrated with a boss (usually after a few deaths).
In the original Unreal I was very miserly about ammo at first. Some enemies could be safely taken out with the dispersion pistol and lots of dodging, so I did. Brutes, Kraal, gasbags, hissticks (as my brother and I called them). Pretty much everything except Skaarj, who dodged the dispersion blasts and had powerful melee attacks or actual guns. Also Sliths because screw those guys.
But titans *definitely* qualified for dispersion pistol pacification. It was tricky sometimes, and took a while, but was so satisfying.
Oh and Sunspire was particularly rough for us. Pretty much the whole level is pitch dark, and we got lost a lot, so we hated to use up the limited stock of flares. What if we've already been in this room? No, instead we used the dispersion pistol as a flashlight. A desecrated temple illuminated by lightning-like flashes of blue light, infested with pouncing spider-like enemies who strike from the darkness. And since the gun had regenerating instead of infinite ammo, whenever we finally found the direction of progress we'd generally be nearly out of charge and have to flee down the darkened corridors we'd been lost in. It was creepy and fun!
We also got used to playing without sound to avoid waking our parents, since we weren't supposed to be playing it at all. So nowadays I find myself listening to podcasts and movies a lot while I game.