Behind the scenes
The exact year the photograph was taken was originally not known. However, the Indiana Jones and the Last Crusade-novelization states that it was taken the year following Anna Jones' death, which would place it at 1913. This seems implausible as Indy looks younger in this picture than he was in the Last Crusade-prologue. The explanation for this mistake seems to be that the information given in the novelization places Anna's death earlier than what was later established. The book The Lost Journal of Indiana Jones gives an update on the circumstances of the photo; it says that the photo was taken when Indy and Henry moved to Utah, which was 1912.
Indy and Henry looks as if they're about the same age as they are in the first five chapters of The Adventures of Young Indiana Jones, when the characters are played by Corey Carrier and Lloyd Owen. It's interesting to note, however, that the faces on the picture are those of River Phoenix and Sean Connery (The Young Indiana Jones Chronicles didn't start until 1992). Both images are altered to look slightly younger than they do in the movie.
The Lost Journal of Indiana Jones includes another photo, said to have been taken in Princeton, January, 1908. Sean Connery's face is used to portray Henry. Parts of this photo can also be glimpsed during the scene in Indiana Jones and the Last Crusade, when Indy finds the earlier mentioned photo.
When viewing the page for Indiana Jones and the Last Crusade on the official Indiana Jones-website, a small version of a third photo can be seen. This one also seems to show a young Henry with a very young Indy. Sean Connery is not wearing a beard in this photograph.
The original "1912-photograph" is also said to be visible in the background of Indy's home, in Indiana Jones and the Kingdom of the Crystal Skull.