The sticker inside the door of my car suggest that tires should be inflated to 2.3 bar (33 PSI). I have usually been driving with 2.4 bar (35 PSI) in my tires. Before going on vacation this year, I increased the pressure to 2.6 bar (38 PSI). Since the car was loaded with my family and luggage this should be about right. It seemed to handle ok.
After the vacation I decided to leave the pressure at 2.6 bar to see if I could increase my mpg. I noticed that the car was not as comfortable to ride as usually, the ride was stiffer. When driving into a bend I noticed that as I turned the steering wheel more and more I would get to a point where the car would all of a sudden turn a bit more than what I was really turning the steering wheel. After a while I decided that it was just too uncomfortable to ride my car with over-inflated tires. When correcting my tire pressure I noticed a bit of damage on one tire. Then I looked closer, I found that the damage was all around the tire at the same distance from the shoulder of the tire. It was most on the outside shoulder of the front tire, but also on the inside shoulder. And also slightly on the rear wheel tires. I stopped by the local tire shop and the guy said that I must have hit something and that the dammage was small and nothing to worry about. I think the real reason is that the tires was so over-inflated that the dammage shows where the tire shoulder was when the tire was at 2.6 bar. I can picture the tire in a bend, and how the smaller area in contact with the road is strugling not to slip. Then it slips or skids a bit and the road tears loose a small part of the tire.
I was not driving enough to make any good data on what the gas savings might be from this, but based on the tire wear and umcomfortable ride, I can not recommend this. Check you tire pressure often. It is well documented elsewhere that too litle pressure increases the rolling resistance and hence also the gas used. So make sure you use the recommended pressure or just slightly above.
Summary in Norwegian: Sørg for å sjekke tryket i dekkene ofte slik at de aldri går under det som er anbefalt. Min erfaring er at +0.1 ekstra også går helt fint. Noe særlig utover det går for mye utover dekkslitasje og veigrepet.