What PSI should I be running on the 20 inch Wrangler tires on the 2007 Dodge Ram?

Mine were at 28 psi. I noticed that the max is 44. I took them up to 38 but seems kinda rough riding now.

Dave in Philly

on the inside of the door, it should say the recommended pressure. i usually try to keep around 32-34 in there.

Yes, on the inside of the driver door should be a sticker with tire pressure ratings. Red

I use 40 #'s in my ThunderRoad but I have 17inch wheels. Ride's ok, I did it for the gas mileage.

The recomended pressure on the door is more for ride quality than tire life. (Firestone & Ford problems)
I live in Florida where the roads a made of seashell blacktop that loves to eat tires. (heat and sharp edges of the shells)
I have found over the years that keeping the tires at the max cold pressure rating on the tires increases tire life by 25% and also increases fuel milage. I also think the truck handels better with the stiffer tire.
Since doing this I have not had a tire come apart on me.
The only drawback is a harsher ride. (if you only care about ride buy a Lincoln instead of a truck)

10% under max tire pressure. 44psi max = 40psi cold tire pressure

I run mine at 42psi front, 38psi rear (empty)...then use a tire tread depth gauge every month or so to make sure that the tires are wearing evenly across the entire width of the tire. If not, I adjust up or down accordingly.

Manual says 36psi, works for me. Was around 33-34 this winter.

The stock 20's, all season? are crappy in the snow/ice. Probably hook up better if I ran 26-28psi, but I don't want to kill the life of the tire, or damage the rim in a pothole.

Higher PSI will increase gas milage, wear out the middle of the tire faster, and give you a stiffer ride. Will hydroplaneeasier as well.