You'd be surprised at what your web browser and operating system cache... That one session where you forgot to switch to incognito mode could leave hundreds of images on the hard drive ;)
Relatively... The browsers themselves won't write anything to disk but this doesn't stop things like plugins (EG: Flash, Java, media players, etc) from writing to disk, or lower level operating system functions (IE: Swap) writing to disk. How likely is it that these will write to disk? I don't know exactly, but it would vary between browser plugins and operating systems.
For example: I use Linux, with no swap, and with few browser plugins and would consider myself fairly safe when in incognito mode.