Zak S posted a mechanic for randomly assigning keys to different doors with a minimum of fuss: tell players when they find a key "it's key 37" (after rolling the number randomly.) The key number is actually the percentage chance that the key will open a door, although it will only open one door.
Nice, and very last-minute-GM-y. But I'd rather not have key numbers; so here's an expansion of what I said in the comments section: use "keywords". When you describe the key, one word in the description is significant. For example, "you find a brass key". The keyword is "brass". Translate that into a number, using the first consonant or consonant cluster (or first vowel, if the word starts with a vowel.) There's plenty of mnemonic letter-to-number codes out there, but I've written about before about the one Lewis Carroll used.
So, the brass key has a 10% chance of opening a door. The iron key has a 3% chance, as does the icicle key.
But! Doors and treasure chests can have keywords, too. Always use the lower number for your percentage; if you use the brass key on the door with the lion engraving, the chance isn't 10%, it's 5%. If the keywords match, multiply by 10: the iron key has a 30% chance of opening the iron door.
Some keys might have two keywords, like the obsidian dragon key. They open two different locks; use the higher number first (in this case, 24%;) once you've found the "dragon" door, use the lower number (4%) to find the "obsidian" door.
If a door has two keywords, just use the lowest number, but you have potentially more keywords to match; the Bone Dragon door only has a 1% chance of being opened by most keys, but the bone key or the obsidian dragon key each have a 10% chance of working, and if there's a bone dragon key, it's 100%. Alternatively, if the Bone Dragon door has two keyholes, you need two keys, one with a 1% chance to find the right key, the second with a 10% chance.
Don't like percentiles? Only use the first letter, and use that number as a Target 20 modifier. So, if you try to open a door with a key that has a decorative snake wrapped around the shaft, roll a d20 and add 6; if the result is 20 or higher, the key belongs to that door. For matching keywords, you'd want to add 10 instead of multiply by 10.