My first decent car was the Corvette Z06, but I couldn't afford to fully mod it before the oil change, and the max HP I ever reached was 799. It's since dropped to 795. I decided to go ahead and try a new Z06, fully mod it, and then do the oil change, and it was above 800HP.
On some cars... the HP actually goes up as you drive it. Two cars I know that work this way are the Corvette Z06, and the Mazda Miata LS. The quick and easy way is to race some test tracks. Don't change the oil after every race, I got the Z06 up to 811HP before I got tired, and quit the game without saving. The Miata LS was totally stock (for the endurance race), I think I saw a max HP of like 167 or so.
Not all cars gain HP as you drive them though, only a very few.
To get max HP generally:
Buy car new, mod HP to the max, and then change oil before putting any miles on it. Most cars don't lose HP until about 500-1000 miles I've found. Generally the cars with turbos lose a bit after 500, and NA cars lose at about 1000. The Mazda Rx-7 has a max HP of 709, at about 500 mine started losing HP, it's down to like 702 now.
-Morgan