SHAKE IT UP
In making generators, one wants to have sufficient variability and complexity. Here's a few methods I've found to help make generators more complex, interesting, and variable. Though it's a mix of science and art, these tips may help you "shake up" your generator designs so you get more complex and interesting results.
HAVE ENOUGH DATA
Goes without saying. I've said it before, I've said it now, and I'll say it again. Get used to it.
In all seriousness, the data usually is the place where you can produce the most variability for least effort. If your data structures are well-arranged, then good data pays off.
HAVE DEGREES WITHIN
OR VARYING DATA
In some cases, you can make a trait or element of a generator more variable by including "degrees" of certain properties.
Consider the properties of color. You can have red, blue, yellow, etc. But why not dark red, light blue, and very light yellow? Combine "degrees" of common colors with more "creative" color names (crimson, cerullian, ochre) and you've taken a simple trait and made it diverse and even poetic.
There are other areas you can experiment with degrees: height, width, temperature, expense, etc.
REDUCE YOUR RESULTS
In a generator, you do not necessarily have to cover all ground.
This is going to sound very strange, but sometimes showing a large amount of detail actually backfires:
What you do not include in a generator can say as much as what is included, and gives room for people's imagination to work. Though this may sound strange since I trumpet the Tons of Data approach, this is actually about varying the structure the data is used in.
Let's say you're making a generator for Barbarians (hey, always popular in any genre), and one of the things you want to include is favorite weapon, favorite defense, and favorite combat approach. That's fine, but might not some characters not have a preferred weapon (hey, if I was a Barbarian I'd learn to fight with anything at hand), or a preferred tactic (maybe they're good, maybe they're unimaginative), etc. Varying the kind of data returned could be:
You've taken one area of return and made it so it has six possible results. Sure you're not defining anything, but this lack of definition can say volumes as well. If your Barbarian's favorite weapon is the warhammer, he has no preferred method of defense, and likes direct assaults, then that means he's either very good, very crazy, or likely very dead. The gap has become meaningful with a little applied imagination. The nothing can mean something.
PRODUCE POSITIVE RESULTS
Some generators include too many positives - what about negatives?
Perhaps your magic item generator created a neat magic sword - but are there any side effects to using it? Maybe you're devising a character generator and have favorite food as a result - but why not include what they don't like?
Negatives create as much flavor as positives, and interacting with positives, can draw richer, more complex pictures. If that magic sword of dragonslaying causes its user to become obsessed with it, there's rich story potential and backstory potential. If a character loves potato chips but despises popcorn, there's probably an interesting reason.
You can overdo these, so keep in mind the above rule about creating variance in generators. Varying the interactions of positives and negatives can prove quite worthwhile.
ADD IT ON
You have a Gem Generator that makes "red gems" and "blue gems with strange white swirls" in them. Fine, but you can take it farther. Do they chip easy? How are they cut? Heavy or light? How do they react under UV light?
Now, as noted above, you may not NEED all those details. But they're details you can consider to shake up a generator. You may have a result, but how far can you take it, how much diversity can you add to the basic data.
If there's often a problem in variance, it's this one - not sameness, not lack of negativity, not inclusion of exclusion, but not pushing things far enough. In fact, if you don't push a generator far enough, you won't even get the chance to screw up in other ways!
The Gem Generator example is a good one - gems can have different cuts (or be uncut), properties, etc. Learn to include properties, traits, and elements that are appropriate to your generator's topic. Study up on the subject.
Then, when you've added on, use most of the previous suggestions to make maximum use.
Good luck on "shaking up" your generators!