As large cities go, generally people in Tokyo are polite and try not to push and shove. However, with the sheer number of people on the streets & on public transport, and the rush that people always seem to be in, you do get bumped into occasionally.
In an attempt to improve this, the Japan Ad Council is running a campaign with the slogan “Tokyo is a place for smart and sophisticated manners”
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In case you can’t read it:-

Glance of appreciation:

When you’re in a hurry
Someone lets you pass
Gesture thanks in your glance

Edo Shigusa (the subtle gestures of Edo) were fruits of the wisdom generating from cohabitation in a densely populated city. For the Edo people, subtlety was a definite virtue. The public manners of Edo were considered to be sophisticated mannerisms of cosmopolitan people, … which applies to modern Tokyo

Not sure this will have any effect, but it’s nice idea.

I remember while living in Spain, in an attempt to improve the manners of drivers, there was a campaign to make drivers stop at red lights and pedestrian crossings. Volunteers would wait next to a crossing with a whistle in their mouth and a placard. Whenever a driver infringed, they would jump out, blowing the whistle and brandishing the placard.

Will we have politeness police on the streets of Tokyo one day?!