Though the great majority of Nara's 1200 sacred shika deer are very gentle, one must always remember that deer are wild animals and can act aggressively or unpredictably if it suits their interests -- and one never knows what a deer considers his/her interest to be. One thing for sure -- they have a god complex when they get hungry!
Most of the time, the issue has to do with the deer crackers (shika sembai), which, appropriately enough for sacred animals, reminded me of childhood communion wafers back in 1970's Waterbury, Connecticut. Y150 can by you a stack of joyful animal feeding, with fawns and does gently licking crackers from your hand. However, Y150 can also buy you aggressive and hungry males sacredly snapping at every move of your hand. Julia is not the only person I know to have been bitten by a deer at Nara!!
My recommendation: Keep your head high and don't let too many males crowd around you. I'd keep children under 40 pounds or 4 feet tall under close supervision around the deer.
There are some wild deer in the Nara Park. They are pretty and sweet but so very hungry and they like to eat paper, cloth, your fingers etc. If you give them something, they'll never leave you alone. Try to keep all you papers out of sight, close your bag and simply try to ignore these and let someone else get in trouble with them.
Deers wander around freely in Nara Park around the Todaiji and Kasuga Taisha. Vendors sell shika senbei (deer biscuit) for Y150 for you to feed the deer. Once you start feeding a deer, others will come and flock around you. If you are wearing delicate clothing, be careful because a deer may just bite at your clothing to attract your attention!!
The downside of the herd of deer in Nara Park is the poop. It's everywhere, despite any and all attempts to keep it under control. The other edge of the danger is that in Nara you're always looking at the pretty stuff, so you often forget to watch where you're stepping. If you are wearing shoes with lots of depressions, get ready to scrape the stuff out. If you're wearing totally flat soles, don't trip!
The male deer can get pretty agressive in the Fall as my 5 year old found out (butted about 3 metres!). He was in tears in the Spring when we went back for another visit, and had to be shown that they were no longer agressive, but we were still cautious.
Before you start feeding the deer in Nara's parks. Know that - after getting something - they will follow you around for long long time. Beware that you do not have potential food visible, as when they get the chance, they will take it (also when later it seems to be a handbag or something that looked like a nice treat).
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The deers are cute but can be threatening in their quest for food: if you're carrying a plastic bag they will try to snatch it from you. Small children eating ice-cream or cookies are an easy prey, so especial care should be taken with them.
They're pretty aggressive. If they think you have food they'll come right up and nibble on your purse or clothes.