We have a 2008 Fit, and just had to replace the battery at 45k miles. It was working, but not holding a full charge, so bound to fail some day and I didn't want my wife to be stranded. My nephew has the same model year Fit, feels similarly, and they have more miles on theirs than we do on ours.
Outside of this, and tire issues due to a nail, this car has only needed routine maintenance. Overall we are very happy with it, though the carpeting could be more robust - the carpeting in my 1993 Ford Escort seems stronger and like it will last longer than that in the Fit. If it is offered when we need another gas miser down the road, it would be first on my list to check out.
It gets really good MPG, and has much more power than I thought a 1.5l motor could get from an automatic transmission.