The key phrases to remember with Kanban are 'visualise the backlog' and 'limit work in progress'. For this reason I think Kanban is best managed using a single board. Otherwise people find it hard to visualise the total amount of work that needs to be done or that is currently in progress. Multiple boards also make it harder to set hard limits on the total number of tasks that the team can have in progress at any given time because you'll need to count up the total across several boards to keep track.
To manage multiple projects (or even themes within a single project) I use swimlanes to visually split the work out but keep it on the same board e.g:
----------------------------------------------
| | To do | In progress | Done |
|-----------|-------------|-------------|------|
| Urgent | T-69 | | T-6 |
|-----------|-------------|-------------|------|
| Project 1 | T-103 T-204 | | T1 |
|-----------|-------------|-------------|------|
| Project 2 | T-30 | T-97 | T-12 |
|-----------|-------------|-------------|------|
| Project 3 | T-465 T-500 | T-34 | |
----------------------------------------------
That way you can set per column limits for total workload rather than per project, and you can get an instant visual representation of the total number of tasks in each status.
This can, of course, become quite unwieldy, especially if you're using a physical board. I use JIRA Agile to manage the process, using Quick Filters pretty heavily to quickly switch between views of the work.