Assuming I have no known mechanical problems, at what mileage should I replace the timing belt in a 2003 Honda Accord EX V6?
I have heard 60,000 miles from some sources, but the manual seems to suggest around 90,000 depending on driving conditions.
What are your driving conditions? If you primarily do city driving (stop and go, dusty) or live in a particularly hot or cold environment, then it's worth looking at the "severe service" area of your manual, and go by that recommendation.
Usually, it's relatively easy to inspect the timing belt by taking off the top part of the timing belt cover. You are looking for signs of obvious distress, cracking, discoloration, etc.
Another consideration is whether or not the engine is an interference engine. If it is, a timing belt breaking means Very Bad Things. If it is not, it just means you will break down and need a tow.
Edit - After more research, the evidence suggests that the Accord V6 IS an interference engine. Hopefully someone who has access to the Honda technical reference manuals can confirm this. I removed the link I had earlier, because looks out of date (nothing newer than ~1995). Finding reliable database of interference engines on the Internet is surprisingly hard.
The manual states that for a 2003-2007 Honda Accord, the timing belt should be replaced at an 8 year or 105,000 mile mark. I just inherited a 2004 Honda Accord EX-V6 sedan from my father who purchased this car new in 2004. He drove a total of 55,000 miles in the 8 years in which he owned the vehicle. I feel stuck because I don't want the belt to snap off, causing severe damage to the valves and pistons, but I also don't want to replace a perfectly functioning belt with 50,000 more miles of service left. I would inspect the belt and if you see any kind of cracking or fading of any kind, replace the belt, especially if you are already oncerned and aware that you need the timing belt serviced.
Here is a detailed DIY for the Honda / Acura V6 J Series Engine for replacing the timing belt: