Wandering monsters have been a fixture of D&D since the beginning. I can't even begin to explain how or why Gary included them. Did his players have a tendency to dither outside dungeon chambers? Was he bored and looking for an excuse to throw a gelatinous cube at the party? Who can say?
(Well, I'm sure someone can say, and if they want to roll in here and say it, fire away!)
My old gaming groups never used wandering monsters. There was enough adventure in the rooms of our dungeons, and enough of our adventurers took place in urban settings, that we never saw the need for them. The resource model for earlier D&D editions was such that, from a strictly mechanical perspective, each wandering monster meant one fewer monster the group could handle before heading home.
Wandering monsters do add the element of the unexpected for both players and the DM, and there's always the chance that something cool and memorable happens when you add situation A, condition B, and wandering monster roll C.
The interesting thing to me is that, of all the versions of D&D, 4e is perhaps best suited to make the most of wandering monsters. The characters lean heavily on their ability to take short rests. Wandering monsters are a spanner in that works. To wit:
When the characters take a short rest, roll 1d20. On an 19+, a wandering monster stumbles across them at some point during their rest.
(Insert a table of wandering monsters here, based on your adventure.)
Voila! Each time the PCs rest, there's a chance they fail to regain their precious encounter abilities and hit points. Instead, they're looking at a mob of angry critters. Even if the party is safely holed up in a room, and the monsters pass them by after a few tense Stealth and Perception checks, you've added a compelling element of uncertainty, danger, and chaos to the adventure.
If you want to get fancy (and who doesn't want to get fancy?), you can tie your wandering monster checks to a skill challenge. Let's say the check starts at 15+. Each success in the challenge bumps that threshold up by 1, each failure drops it by 1. You could use Perception, Stealth, Streetwise, and so on, along with judging the PCs' actions in the dungeon, to manage the challenge.
So, time to dust off those old wandering monster tables. They're more useful now than ever.
22 hours ago