Roughly 8 years old by stander-ed, but it would appear that they can come in at any time if allowed.
Kakashi and Yamato graduated at the age of 5, so there is uncertain if the is a age limit.
Besides age, the general situation of the village can sway the graduation rate. When ones like Kakashi, Yamato, and others graduated, Konoha was in the middle of war, so they needed what talented shinobi/kunoichi they could get as soon as possible to bolster their numbers. However, during the time of Naruto we knew at the beginning, it was in the middle of more peaceful times, thus not nearly as high a need for them to graduate so quickly.