Random is Good
First, let's talk about how random tables are used. *holds up spork*
Sometimes a random table is used more for information or inspiration, rather than to actually generate a random result. (I'm willing to bet that most people use The Dungeon Dozen to cherry pick brilliant ideas (and there are tons) than to actually roll on it during a game session.) In this sense, it's just a broad palette of colors presented to the DM, like a menu. (That's why I like Elfmaids and Octopi, too.)
As a way to present information, it works great. And you can always roll on it and challenge yourself to use whatever comes up.
This is almost the same as #1, except it's used to deliver information. A table of "d6 townsfolk and their houses" would primarily be used as a listing of the town's inhabitants. Only would it possibly be used to generate a random townsfolk (or a random house) if the party starts jumping in random windows.
Again, this is a good way to present information, and has the added benefit of extra functionality if you ever do need to roll on it. Yoon-Suin's setting information is presented almost entirely in tables. It's one of the books best features, since you never have to read the same thing both in the summary and again in the table. ASE 1, too.
People use random tables to track the untrackable, like where each NPC is at any time in a city. The game only cares which one you bump into next. It tries to mimic a chaotic, complex system (people or monsters moving around an area) through a simple process. It also sometimes gets labeled as "realism".
You sometimes see people making encounter tables based on a 2d6, so that some entries are more common than others. The idea being that you will encounter wolves more often than Sparthak the Headless Ogre, since there are more wolves, and only one Sparthak, and the tables should reflect this.
I have some objections to this usage, which I'll talk about below.
I'm not talking about keeping it fresh for the players. Whatever happens, the players don't know if it was scripted / written as part of this room, or if it was something that the DM spawned from a random table.
What really matters is keeping it fresh for the DM. When you use random tables, the game develops a miraculous ability to surprise you, the DM, with the variety of situations that develop, especially when results from random tables start interacting.
If you feel tired of DMing, try leaning on random tables more. The game becomes chaotic, surprising, and fresh again. And you are right there, discovering it simultaneously with your players. You feel more like a player, and less like a scriptwriter.
This is one of my favorite things about OSR gameplay, actually. The willingness to pull from a random table and accept the results, no matter how much or how little chaos it spawns.
5. Expand Coverage
Do you feel like writing entries for all 200 hexes on the new hexmap you just drew? No? Well, you should write up a random table that covers them. This works well because your players will move across the map in a way you can't predict, and they probably aren't going to visit all 200 hexes.
The same principle is true if you don't want to write up all 666 layers of the Abyss. You could write up a d20 table of specific layers, or you could write up a recombinant generator that uses several subtables to generate the layer.
Random tables are the key to sandbox play, because that's what you reach for when your players wander off the written path. That's also why you can't "derail" a sandbox game. The DM just reaches for the stack of random tables at her elbow and says, "You want to steal a boat, huh? Well, there are two ships in the harbor, and they look like this. . ."
Random Is Bad
Here are reasons why a random table might suck. *puts down spork*
I know I listed this as a strength, but I think it's more of a weakness. Sure, it makes a game feel realistic, but if you wanted realistic, 98% of all the DCC level-0 funnel characters would be farmers. Instead, DCC makes the much smarter choice to throw that out the window and use a much more interesting variety of careers instead.
The same is true if you are using a 2d6 for your random encounter tables. Why not use a d12, and let your players bump into a wider variety of things, with a smaller chance of repeat encounters? If you want one of the encounters to be very rare (1-in-36, for example), I'd ask you to make up your mind. Do you want this thing to happen, or not? If yes, then make it likely. Most groups that run the adventure aren't going to find it, otherwise. If not, then cut it.
Plus, flat probability curves have more entropy than a pyramidal (2d6) or bell-shaped (3d6) curve. Only paladins are afraid of a little chaos.
2. Too Big
If your players are only going to bump into an average of 3-4 of these entries, do you really need a d20 table to contain them? Yes, a big table is still useful for Inspiration and Information, but think hard about whether some of that stuff would be better presented somewhere else.
So, if you have 20 entries, why not trim them down to the 6 best ones? Which brings me to. . .
3. Variable Quality
Sometimes I see a d8 table with some good entries and some shitty ones, and I wonder, why not just ditch the shitty ones and keep the better stuff. Knock it down to a d6 or even a d4. Distill that brain-brandy into a higher proof.
If you want to keep the shittier ideas, you could mention them elsewhere so that the DM can still use those ideas if/when they restock the random table. Or heck, you could even make a Table Restock Table if you were feeling saucy.
I also have mixed feelings about randomly generated dungeons. On one hand, Castle Gargantua and Scenic Dunnsmouth are awesome. On the other hand, I can't shake the feeling that they would be better if they were static. A fixed adventure allows for better spacing, pacing, and dramatic delivery (you know, like finding blood-drained victims before you find the mouthless vampire lord with symbiotic stirges nesting in his ribcage). Using randomly-generated adventures doesn't seem to solve any of the problems that random tables can solve, except Freshness, which seem silly because (a) there's enough variance in adventures to keep it fresh for the DM anyway, and (b) it sacrifices a lot of good structure opportunities.
One of the biggest complaints that gets made about old-school games is how random the random encounters are.
The rooms all have interesting monsters doing interesting things that reveal more about the history of the dungeon, and give useful clues, while wandering monsters do none of those things.
And so I say, make your random encounters less random. Connect them to other parts of the adventure. Detail the entries for wandering monsters as if you were detailing a room of your dungeon. If you have a table for "random fellow prisoners", then make sure that some of those prisoners connect with things outside of the prison. I tried to do that exact thing here.
Just Kidding. Random is Spork.
If you are one of my rare readers that doesn't already make extensive use of random tables, go try some!
If you are writing an adventure or whatever, tighten up your tables! Polish them until they bleed sparkles. They really are one of the best parts of the game.