I constantly find that I have no change. Right now my wallet contains some notes, plus one $2 coin and one 20 cent coin. And having discovered this, I'm going to take the 20 cent coin out and set it aside for use at the laundromat, where it costs $2.20 per wash.
Five years ago, change used to build up in the bottom of my wallet, and often when I went through it I had fifteen dollars or so just in coins. (Australia has $1 and $2 coins.)
But then I went to the US. Immediately the change problem got way worse: America still has 1 cent coins (the "penny"); they have a 25 cent coin (the "quarter") instead of a 20; and the 5 cent coin (the "nickel") is bigger than the ten cent (the "dime").
It's amazing how much harder it is to make change when there's a 25 cent coin. In sensible countries, you can decompose the problem of making change into two simpler problems: one for the tens digit, and one for the ones. In Australia, the ones column is made trivially easy by the fact that we did away with 1 cent and 2 cent coins; anything below the 5 cent mark gets rounded. But in the US, it's trickier -- if something costs 87 cents, say, you don't instantly know how many 5 cent pieces you should give. You have to subtract off three quarters, which leaves 12 cents, which takes the form of a dime and two pennies. (Confusing, isn't it?)
To make things more confusing, sales tax is applied after the listed purchase price. So if you buy something that's listed as 99 cents, you'll be charged, say, $1.07. (Note to Americans: Australians think this is just plain crazy. The price marked should be the price charged.) And sales tax is a state tax, so it varies from state to state. An it's not always an integer number of percentage points. All this adds up to make it all but impossible to tell how much something is going to cost, until the checkout chick actually tells you the number.
So where in Australia I can easily fish out some coins to make part or all of the change, in the US it's much harder.
Unsurprisingly, in the first year or so that I was in the US, change built up in the bottom of my wallet enormously. Pennies are particularly problematic, especially since there's no 2 cent coin. You can thus receive up to four pennies in a single transaction. I wound up with a small mountain of pennies on my kitchen counter.
Incidentally, examining the dates on a random selection of US coins reveals that pennies are on average substantially younger than the other coins. This is because they stay in circulation for less time before dropping away unnoticed into some worthless jar or drawer. (And I wonder how much it costs to mint replacements?)
So the first trick to change minimisation is to always have at least two or three pennies rapidly available, semi-spilled out of the wallet's change pocket. It's easy to figure out how many pennies you have to give away in order to receive none back.
This doesn't take care of the nickels and dimes, but after a while I got the hang of those, too. The more of them that you have in your wallet, the more are likely to be at hand when you spill forward a random selection of coins, so once you've built a lookup table in your head to do the modulo-25 arithmetic, the problem self-manages. And quarters are actually useful, for soft drink machines and laundromats and the like.
As another aside, this problem is evidently not unique to foreigners like myself. Change counting machines, although pretty much unheard of in Australia, are quite common in the US; in supermarkets and the like. You take your jar of small useless coins in to the supermarket, pour it into the machine, which counts it, keeps a percentage for the house, and gives you the rest in real money. (Actually, to keep the design of the machine simple, it generally just prints you a voucher which you redeem at the cash register. And of course, the voucher is for some irregular sum of money, so the checkout chick gives you some more useless change in return for your original useless change, which you can then drop straight back into your jar.)
The upshot of all this is that I now obsessively dispose of coins at every opportunity, at a rate designed to keep a US wallet in balance; and thus, here in Australia, I never have any change at all.