I run recommended pressure if it has the original tires but once they have been changed, I base the pressure I run depending on the max rating on the sidewall of the replacement tire.

I put 32psi in tire that is 35 max.
44 max gets 40psi.
51 max gets 45psi which is what I currently have on my 2000 Neon.
Why should I run 32psi on a tire that is 51psi max? I'll take the MPG a higher PSI provides over a softer low pressure ride.