It's been 3 days since the massive earthquake, we don't see any kind of riot or disturbance in Tokyo, more than 200 miles away from worst disastrous area, Sendai.
But some people may feel panic themselves.
I found cars making extreme long queueing at some gas stations and some others showed petrol was sold out, though Petroleum Association (PAJ) announced that petrol shortage wouldn't come up in Tokyo. If they would go to gas stations as usual, there wouldn't be petrol sold-outs.
Also found electricity generator, petrol cans are sold out in a home center. Electricity generators are not cheap, they should cost around 80,000 yen or more (80,000 yen is nearly equivalent to 1,000 US dollars).
As one of gas tanks in Chiba, near Tokyo, has been burst into flames and destroyed, some people may feel that petrol privation will occur.
Emergency goods, such as bottled water, instant foods, dry-cells, and so on are almost sold out but maybe it's not a surprising case.