Such as when traveling by air or making expensive purchases. There's nothing so satisfying as plunking down a sack of pennies when purchasing stuff and saying "just let me know if it's not enough."
The above is sarcasm. I hate pennies. They are pretty much useless these days. The only joy I get from them is when someone annoys me, I can throw them at the person.
They are so useless, in fact, that it actually costs nearly twice the value of a penny ($0.0183)[0] to mint one.
That said, I'd really like it if larger denomination coins ($1/5/10) were common in the US as they are in the EU. Generally coins with value more than $0.25 aren't used (yes, $0.50 and $1 coins exist, but are rarely used/distributed).
[0] https://en.wikipedia.org/wiki/Penny_(United_States_coin)
Edit: Added forgotten link.
Someone is making a lot of money from the status quo, and they will fight very hard to keep it.
Australia got rid of theirs in 1992.
Whenever I go to the US I try as hard as I can to always drop them in the take-a-penny-leave-a-penny-tray lest my pockets tear from the bulk.