The Water Temple of OOT and Hyrule Castle of TP are the only 3d dungeons in which you do not need all the small keys to finish the dungeon (I think lol, and this excludes replaying dungeons in MM by resetting time- that makes it possible as well).
I'm pretty sure that in Wind Waker and Skyward Sword (and maybe other games- Majora's Mask possibly without replaying dungeons and most recent 2d games) you can never have more than one small key at a time ever (in TP the only time you can have more than one is in Hyrule Castle I believe).
In ALTTP the hookshot seems necessary to complete dark world dungeons 5 and 6 but you actually don't need it. You can actually beat all dark world dungeons except 8 (Ganon's Tower) before entering dungeon 2 (which has the hookshot).
In LOZ you could beat the game by only collecting 5 of the 12 items found in dungeons (raft, ladder, bow, silver arrow, and whistle). The last Zelda game I believe that lets you skip a dungeon item was Majora's Mask in which you could skip the Giant's Mask but technically it might not be classified as a dungeon item.
In the Water Temple of OOT most walkthroughs have you change the water level six times but you actually can beat the dungeon while changing it three times without any glitches.
In the Sandship of SS most walkthroughs have you hit the timeshift stone 7 times, but I've found multiple ways to finish the dungeon by only changing time 5 times. (here's one-
http://zeldadungeon.net/forum/showthread.php?27204-Fastest-Path-Through-the-Sandship)
The Earth Temple of SS has 4 rooms (excluding the boss room) and one of the rooms just has the map so you only have to enter 3 of the rooms to beat the dungeon. This means that the minimum times you open a door in the dungeon are entering and exiting the bomb bag room, passing through the door to the rock cliff room, and opening the boss door.
You can revisit the Skyview Temple as soon as you get the Water Dragon's Scale so that you can give the sacred water to the Water Dragon the first time you meet her.
In the Fire Sanctuary I'm fairly certain you can fail to save a mogma. The one that gives you the map can be left there forever from what I've heard. I haven't done this myself but I know it's possible if you kill yourself to warp back out of the room to a bird statue after getting the hidden small key. (this one I've only heard about and haven't done)
I'm pretty sure the only dungeons that make you collect the dungeon map out of the whole series are the Snowpeak Ruins of TP and Sky Keep of SS (could easily be wrong though).
There's a key in the Snowpeak Ruins that's fairly unique in how you get it. On your first playthrough you practically require the compass to locate it and dig it out of the sand, but on subsequent playthroughs you can just skip the compass and dig it out right away.
Hyrule Castle in TP offers one of the few true branching paths within dungeons out of the whole series (or at least in the 3d games).
Because of the resetting of time in MM, all of the dungeons can essentially be replayed as if they were new except for the dungeon item, map, compass, and boss remains (all keys including the boss key reset). Replaying them can result in different ways to progress through the dungeon. The one I most recommend is Snowhead because the hookshot's ability to attach to torches lets you skip locked doors.
You can beat OOT without doing the Bottom of the Well if you can manage to beat the game without the lens of truth.
Most people realize that you can beat the Spirit Temple of OOT before the Shadow Temple, but you can actually beat it before the Fire Temple as well since the Megaton Hammer only opens up a shortcut in the dungeon.