I'm fairly well read in the benefits and processes of Scrum. I get the ideas on the backlog, burndown charts, iterations, using user stories, and other various concepts of the Scrum "framework".
With that said... I work for a web development firm that manages multiple projects at one time, with six team members that make up the "production team".
How does Scrum work with having multiple projects? Do you still just schedule an iteration for a single project in a certain amount of time and the entire team works on it, and then you move on to the next project with a new iteration when that iteration is completed? Or is there an "agile" way in managing multiple projects with their own iterations with only one team at the same time?
Scrum really doesn't dictate that you have to be working on the one self-contained product. It simply states that there is a bunch of stuff that needs to be done (the product backlog), there is a certain amount of development time available in the next iteration (worked out from the project velocity) and there are items selected by the client/business as having most priority from this pool of issues/tasks that will be done in the next iteration (the sprint backlog).
There is no reason that the product backlog and sprint backlog have to be from the one project - even in a single project there will be discrete units of work that are like separate projects - the UI, the business layer, the database schema, etc. Enterprise software development in particular is like this, where you have a number of code bases that all have to be progressing. The Scrum process - meetings, questions, burn down chart, etc - all work whether it is one project or multiple.
Having said that, in practice it is often good for each iteration to have a major theme - "do the reporting module" or "interface with XYZ system's API" - so that a lot of the issues come from one project or area and at the end of the iteration you can point to a large body of work and place a tick against it.