Earthquakes in Tokyo
Japan experiences 1,500-2,000 earthquakes every year. About 75% of these are minor tremors that do not register over 2.0 on the Richter scale (most people would not notice any movement at this level). Tokyo feels 150-200 tremors each year with 1-3 earthquakes registering above 4.0 (at which point they would be felt by everyone and indoor objects may rattle). Because of this seismic activity building regulations are extremely strict and modern structures are designed to withstand much stronger earthquakes than those that usually occur within the Japanese archipelago.
Safety in Tokyo
Compared with any other major city, Tokyo is extremely safe. While the usual advice about keeping your belongings secure still applies, theft is extremely rare (some Japanese will even save seats with their smartphones and handbags at cafes when they go to use the restrooms).
The only word of caution is for single females to avoid the less reputable districts such as Kabukicho in Shinjuku during the early hours, and use the female-only carriages during rush hour. Sadly, chikan (groping on trains), although rare, is not unheard of.
If something is lost or stolen you should file a report at one of the 24-hour manned police boxes (koban).