The beauty of cards is threefold: 1) They are flexible and 2) they are easy to use when working in a group. Used to manage the sprint, 3) they are part of an extremely easy to understand overview of the state of the project.
So whether you are brainstorming on stories, planing tasks for the current sprint, or reviewing the sprint in a retrospective, cards are easy, let people work in parallel, and a very effective for communicating and prioritizing information. Even now, I prefer to use cards for the Sprint Retrospective, despite their drawbacks.
The drawback of cards are also threefold - reusing data, backup and distributed access to the data. So if you use cards to create your product backlog, that's fine. But now your CEO wants a report on which stories have been completed and which are forecast to be completed by which sprint. Easy to do if you have a spreadsheet, but first you have to enter all the data by hand, a job which usually falls on one person. Related to reuse is backup (and possibly other security issues): what happens if you loose the cards? (Anybody remember what a floor sort is?)
What do you do with distributed teams? Everybody needs to see the task board. In a meeting, everybody needs to not just read, but also post cards on the wall. How do you send the sprint contract to your customer? I have heard of teams using web cams and Skype connections to broadcast the task board to remote sites, but even that seems like a weak alternative. The remote sites have read only access to the cards, if they are even legible...
Using cards to manage the Scrum data (backlogs, taskboards, burndown) does not address how to manage other documentation, e.g. design documents, program documentation. What do you do with the rest?
And finally, how well does the approach scale? When you have hundreds or thousands of stories?
Personally, I use (and love) cards for the Sprint Retrospective and for the initial product brainstorming. For your first sprints, this is a good place to start, if not the place to start, but I think most teams will quickly reach the natural limits of this approach.
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