Very little. Mostly minor, maintenance related problems which I have been able to fix myself.
Had timing belt changed at 175,000. Car now is approaching 215,000 miles, still gets 38-40 mpg on highway.
Bought it with 107,000, hasn't had any problems except doesn't like damp Seattle winters, gets water in fuel in rainy weather, which affects driveability.
This car has been very dependable, comfortable, and sturdy, although with the high miles, it is beginning to show its age. The engine still has excellent compression and uses NO oil, but the suspension rides pretty rough. I would definitely recommend an Accord as a reliable used car.
About the water in the fuel, check the filler pipe for rust, these cars were recalled for rust in there. Check with www.alldata.com for a list of recalls.