The primary benefit of inflation is the manner in which it holds down unemployment. Since it is difficult to reduce wages in nominal terms, positive inflation gives firms an alternative means of cutting costs instead of laying of workers.
Most economists believe any given economy at a given time has a NAIRU, or Non-Accelerating Inflationary Rate of Unemployment, a "natural" rate of unemployment for which inflation is stable and positive.
Inflation lowers the real interest rates in an economy. Low real interest rates encourage investment, as they reduce the cost of capital. Levels of saving tend to be quite unresponsive to interest rates. The last time real interest rates were negative in the UK, in the early 1980s, savings rose, as people had to tuck more money away to have the same amount
Contrary to popular belief, savings DO NOT equal investment in an economy. As any first year econ undergrad will yearn, I+G=S+T, investment equals savings plus the governments budget surplus (or minus its deficit), and that doesn't even include overseas investment.
Inflation does not cause uncompetativeness in international trade if exchange rates are floating, as the currency will depreciate in line with the change in prices.
Some economists believe that continuously low inflation and positive real interest rates have been responsible for the dramatic house price inflation must of the western world has faced in the last 10 years, and the rise in consumer credit and unsustainable levels of borrowing by firms and individuals which have put the world economy into the mess it is in today.
Inflation redistributes wealth from those with high bank balances to those who try not to think about their bank balance, from the old to the young. It makes government debt smaller so in the long run we can all pay less tax. So please think twice before moaning about it.