National healthcare is the best example. I paid about 300 dollars for health insurance for the entire time I was in Japan. Most people I know pay more than that per month for their insurance in the US. When I went to the clinic in town for a cold, I paid about 20 dollars for my visit and meds.
When I cancelled my health insurance at the town hall, shortly before returning to the US, the town clerk told me I had actually paid 18 dollars too much. "I'm so sorry, but it takes two weeks to process the return, so we won't be able to give you this money back before you leave the country," he told me. I assured him that 18 dollars was not a big deal, considering how little I had paid the entire year. "Are you sure?" he kept asking.
Another thing I'll miss: my transaction register. When I opened my bank account, I received a little pad, a lot like the registers that come with your checkbook. I always kept it with me and when I'd go to the ATM to withdraw money, I'd insert it into the ATM. The ATM would update it, so after I'd taken my money, it would print out the transaction, update my balance, and add any other transactions that had happened recently, like deposits to my account or the automatic bill pay I had going for my phone. So every time I went to the ATM, I'd get, free of charge, an update of every financial transaction I'd had, in print on my bank pad. This came in use once, when I needed to prove to my phone company that I'd paid my most recent bill.
Convenience stores are way more awesome in Japan. You can pay your utility bills, buy concert tickets, fax, scan, or print things out. Also, the guy behind the register will definitely take the cap off your bottle of beer if you ask him to.
There's also transportation. Now that I'm back in the US, I'm surprised by all this empty, unused space: huge stretches of unused fields and hills, and towns separated by miles of uncultivated land. In Japan, everything seemed to be on a much smaller, more compact scale. All but the most remote towns are connected by the train system. Even when I drove for hours out into the countryside, I'd usually be surrounded by farmland and factories that were just less densely packed. Usually the only real stretches of wilderness were mountains that were too steep to farm or live on.
Aside from these practical concerns, the thing I'll miss most about Japan is the scenery. It's a beautiful country.