Anyone tugging a wheeled bag with rubber wheels will be subject to a fine up to 500 Euros. Venice residents are exempt. Pneumatic wheels will be allowed but there is no such bag available today.
The Venice City Council enacted the rule after numerous complaints by residents about the noise caused by thousands of tourists lugging their bags. They also said that all those wheeled bags were causing damage to the stone steps and streets.
This, I believe, is the first time a municipality has banned wheeled luggage.
Since Venice relies on tourism for its economy, look for hotels to fight back against this law.
(Be aware, after writing this post I started getting conflicting reports on whether the ban has already been enacted or if the city council still wants to enact it. I’ll keep you informed.)
Addendum 11/24/14–it seems it was all a mistake. Today the Venetian authorities said they never planned to ban wheeled bags. What they are going to ban are large carts that deliver goods and merchandise, not luggage. The local newspaper that first reported on the ban got it wrong.