In any situation (not just RPGs, or even games in general, but Real Life (tm) too), being able to think on your feet is a very important ability to have. Ever watch an improv show and wonder how those people could come up with so many funny gags in such a short time - often with only a split second of preparation? Here's a hint: they had more than a split second of preparation.
"Gasp!" You say. "They cheated! It was camera cuts! It's all scripted, like wrestling and elections! I knew it!"
Whoa there, buddy! Not so fast. There are no camera cuts, or scripts (or shouldn't be, if it's a good show). No, what I mean is that they took time to think up all sorts of funny stuff, and when it fit, they just repeated it from memory. That's the key - improv prep. It sounds oxymoronic, but nonetheless, it's incredibly important.
Take, for instance, a job interview. The whole thing is essentially improv - in fact, many companies ask you weird questions just to see how you react under pressure. However, if you've memorized your resume, and haven't lied on it so you actually know your stuff, the only questions you will be unprepared for are those really, really stupid ones interviewers have no business asking in the first place. In which case, make up some random nonsense and move on.
Knowing your field is one thing, but what if you don't have the time, energy, or ability to memorize every detail of something - say, tables of data? As cool as it may seem (to a very tiny sliver of the population, mind you) to stare off into space, roll some dice, match those rolls to a memorized table, and intone, "You meet a party of 12 goblins," it's impractical. What's more, it can be difficult to switch gears from narrating a dungeon crawl to trying to remember what Monster #37 happens to be... so, don't.
In ACKS, generating a random encounter takes two rolls to determine monster type, (usually) a roll to determine if it's in a lair, and countless rolls (281 dice for a max-size goblin camp!) to determine how many creatures are present. And then treasure rolls. And special rolls. And, if there are high-level humans or demi-humans present, each one needs up to 8 rolls to determine what, if any, magical items it owns. And don't even get me started on NPC parties!
To 100% improv an encounter (and follow 100% of the rules) can be super tough. Even if you're quick with the dice and tables, you're still going to leave a lot of long pauses: "You stumble across, [roll]... uh... a dwarf... [roll, roll]... vault... [roll, roll, roll, roll...]... and there are 116 of them. Plus, oh, a leader, and [roll] three bodyguards, and [roll, roll] a cleric, level... hang on... [roll] 4, I think, no plus one that's 5, and a... [roll] never mind, but they have [roll]... [roll, roll] 5 war dogs, and, uh, 9 sub-leaders, and, oh, divide... carry the... um... eh... a bunch of women and kids and stuff. Wait, what do you mean you just sneak back the way you came?
At that point, you might as well leave your group to call for pizza while you mumble and roll. It takes a long time. Don't do that. Instead, come up with some pre-made things, dump 'em in a list, and roll from that list. If the party runs into something that isn't on a list, throw something simple together - if it happened to be dwarves, force it to be a single company, not a whole vault. It makes a lot less dice rolling, and a lot more action sequences.
But wait! What about the title, Improv Generators? What does that mean?
In many cases - comedy, say - there isn't a lot of room for consulting a computer. It's just too fast paced. But in an interview, you can head off many questions by referring to your resume - "As you can see under 'experience' on page one, I've worked with those tools for about 8 years." RPGs can have the same sort of thing - or even better! I've created an extensive spreadsheet that takes all the information from those random rolls and put it into a single page. Instead of rolling countless times, just select the terrain and... done. It automatically makes all the various rolls, and compiles the information onto a single page. Copy, paste, it's in your notes - five seconds of work, and you're ready to go. It doesn't matter if it's creating a single wyvern or a full NPC party - one click, you're done. Granted, it took a lot of effort; like your resume, or list of witty puns, a random generator takes time to create.
But again, RPGs aren't the only place where a random generator helps. I've idiot-tested program inputs, filled databases, even written stories using random generators. Random data gives you a jumping-off point by doing some of your work for you. You don't have to use the results, but it certainly can be useful - one random group I generated ended up being a mage, carrying a bit of money and four tents, and four low-lever fighters. Random is as random does, but I used that silly information to make a little story - the mage, it seems, is a bit obsessive, and wanted to make sure he never had to worry about being wet if it rained. So, he packed four tents, and little else. If the players run into him, he'll likely be yelling at is henchmen to set up his back-up tent (from the comfort of his first ten, of course). It's silly, and it's fun, and it's not something I would have created otherwise.
And, even better, making words on a page fit into a structured program (be it a huge computer program or five cells on a spreadsheet) helps you understand the data. Today, I could probably roll up an encounter in under two minutes, given access to the right tables, because I understand what the tables say. I've had to manually translate from "Giant Shrew" to "Varmint - Shrew, Giant", or from "Pirate" to "Men - Pirate (River)" to make the creature descriptions line up with the rolled values. Not difficult, but required if you want to match the number you rolled to an actual creature description. I also had to discover how many dice were rolled; a goblin encounter in the wilderness, for instance, has a 40% chance of finding a camp, which contains 1d10 warbands, which each contain 2d6 gangs, which in turn contain 2d4 creatures. Which means you may find a camp with a single warband, consisting of two gangs, which have only two goblins each (plus the assorted leaders)... or, you may find a camp with 10 warbands, which have a total of 120 gangs, containing a total of 960 goblins. And leaders. Understanding how all that works together, and how to make a random generator, has given me a result that is greater than the sum of its parts: in creating a random encounter generator, I've gotten a generator and a working knowledge of the creature list.
That's a lot of words to say that I've written some random generators, but as it turns out, I'm a big fan of random data as a creativity tool. Just like scribbling on a page and filling in holes to make a neat picture helps you make art, or randomly shaking a bunch of letters in a box and making words from them helps you spell and increases your vocabulary, making a random generator for your project helps you learn the rules while giving you story-hooks. Win-win!
Last, but not least, is something that is quite important to me personally: not being caught off guard. If my players want to suddenly abandon a quest and veer out into the wasteland, or drop everything to buy a boat and go fishing, I'll still have encounters for them. Click... you ran into two were-boars! Click... a pirate ship with 75 sailors on board! With this, I am prepared for every eventuality... including the eventualities that I'm not prepared for. Take that, Batman.