I just finished Super Mario Galaxy, causing me to reflect briefly on all the times that I have rescued the Princess from Bowser's clutches.
Personally, I count eight.
Super Mario Bros.
Super Mario Bros. 2 (J) aka The Lost Levels
Super Mario Bros. 3
Super Mario World
Super Mario 64
New Super Mario Bros. (DS)
New Super Mario Bros. Wii
Super Mario Galaxy
Edit:
I saved the Princess in the Super Mario Bros. Special rom patch/hack of the Hudson Soft version of Super Mario Bros., too.