Well, once we get some real data compiled, the story looks a little different.
My go-to site for long term reliability is:
http://www.dashboard-light.com/
They figure out a reliability rating for each vehicle based on the percentage of significant issues with engines or transmissions of used cars sold through dealer auctions. Ratings are further adjusted by percentage of high mileage vehicles and by the age of the vehicle to try to give a fair comparison
Chart comparing Quality Index Ratings of all manufacturers:
http://dashboard-light.com/vehicles/...s/QIRAlpha.png
Honda (+Acura) and Toyota (+Lexus and Scion) do quite well. But so do many GM brands.
The other chart comparing all the manufacturers that I find quite telling is the chart showing percentage of vehicles over 180k miles.
http://dashboard-light.com/vehicles/...s/Over180k.png
Again, Honda, Toyota, and GM all fare well.
Finally, you can go find specific models of cars to see over the years which to avoid. For your Accord:
Honda Accord Reliability - Dashboard Light
Well, it doesn't go back far enough, but you can see a trend of reliability problems (worse than industry average) until about 2003. My generation of Civic has a similar but smaller spike, with models afterwards showing a significant improvement.