I went out today and took over 75 photos with my Nikon Coolpix P100, but I didn't have a memory card in my camera. I'm now unable to retrieve any of the photos - is there any way to recover them?
According to the manual for your camera it has approximately 43MB of internal storage.
This is unlikely to be able to store the number of pictures you took but, if the instructions in the manual are followed, you may be able to retrieve at least some of the missing pictures.
Page 24 of the manual states that any images on the internal memory can only be accessed if no memory card is installed. So if you installed a card into the camera before trying to retrieve the images, you will need to remove the card to see if anything was stored in the internal memory.