Try Starbucks and Chapters. Chapters is on the edge of the market. Starbucks have srung up all over.
Last I checked you have to pay a ridiculous amount for an hour.
I overheard that Bridgehead is free wifi. Also if you ask nicely the westin hotel bar.
The public library downtown (Laurier/Metcalf) has free wifi. At the service desk you have to register for a Internet card, all you need is a photo ID.
Bridgehead indeed does have free wifi: http://bridgehead.ca/ (as well as tasty fair-trade coffee and snacks, and a few locations around the city)
Some of the smaller restaurants likely have it too. There seems to be a list here: http://www.urbanspoon.com/t/250/14/Ottawa/Free-Wi-fi-restaurants although I admit I haven't tried most of those places.