Having been a Scrum coach and an Agile practitioner for more than 6 years now, I can tell you that we encourage physical boards for their ability to produce better team interactions and electronic tools for their ability to effortlessly track performance metrics. As an information management and measurement tool, physical boards are mediocre at best and certainly can't compete with electronic tools. As an interaction tool, they are far superior.
Why Physical Boards are Better for Interaction
In stand ups and planning sessions, physical boards are more fluid and less clunky than electronic ones. Changing the board simply involves walking up to it and moving things around. You don't have to be logged in at a computer to do it, there's no refreshing, synchronizing, or other technology induced awkwardness to deal with. It just works, and when you have a co-located team everyone can see it and change it in real time.
Of course when you have a distributed team and few (if any people) occupy the same space, a physical board will likely not be maintained and go to waste quickly. Like everyone else has said, do what works for the team and their current situation and if you can be co-located, the certainly do.
Why You'll Want Both
Now, I'll tell you why you really want both a physical board as well as an electronic one. You want the physical board for the effortless interaction, you want the electronic one because it can help your team track and improve its performance data. The synchronization tax is worthwhile and actually pretty minimal.
Recording precisely when tasks are moved by whom and what the impact on the related story is would be silly to attempt in any other way but by using an electronic system. In the perfect co-located world, maintain the physical board and sync it with the virtual one so you can see trends and do analysis on your data to understand bottlenecks and continually improve your team processes.
Consider Media Richness Theory
I like and completely agree with the other commentary on non-verbal communication and its importance. This falls directly in line with what we know about media richness theory - that some mediums of communication are more capable of conveying complete information than others. You have to choose, given your team's unique constraints what the richest available method of interaction is while recognizing and hopefully compensating for the costs of the method that you choose.
Make Your Physical Board the Easy Way
If you want the benefits of a Physical scrum or Kanban board without the headache of making one with whatever you have laying around the office, consider getting a professional, ready-made Kanboard from Kanboard.com. It's perfect for getting going quickly.