My 2004 Tundra has the 4.6L engine, 4x4, Access Cab model (7,000# capacity). Does really well with my 2400# pop-up with gear in the bed and a family of 4. I can pull the continental divide on I-70 easily at 60-65MPH which is the speed limit for most of that climb west of Denver. I've pulled the trailer at 10,000 feet elevation without problems.
I've pulled 5,000# moving trailers with no problems too.
Toyota started using the new SAE J2807 standard to determine the towing capacity in 2010. It is generally believed that the J2807 testing will end up reduce the towing capaicty of the domestics (which may be one reason they haven't started using it yet).