If organizing teamwork along the Agile method means self-organization into working groups, own task picking (pull model), and own task management — the questions of whether a manager for those teams is needed at all is indeed a valid one.
While the core team are getting busy with planning, research, development and testing, all the less visible tasks that escape their focus remain to be...managed. This may not be true of the very small teams, in which roles are interchanging and all aspects of the business are held by a compact team. But in medium to large teams, there are some key areas that need looking at by a manager, specifically.
Team & Performance Management
Despite the fact that people pick their own tasks, it's advisable that someone oversees how the work spreads and whether the distribution and assignments are making sense — meaning the big picture. Self-organization does not necessarily imply organizational intelligence, does it?
An integral part of this is making sure that the performance stays on the desired level and of a sustainable pace. The mere fact that people are picking up tasks and doing the work does not yet mean they are getting results and in the needed time-line. Although tricky, the manager's job here is also probing the team's very Agility, best done with typical Agile metrics, such as Lead & Cycle Time, Cumulative Flow or a Burn-Down Chart.
While your team are getting along their own set agile route, it can often be that other company departments do not keep up. A go-between in the form of a manager is the quickest and easiest way to go to join the two, by involvement of proper perspective and foreseeing any impediments stemming from the difference in process stages that different team are at.
A similar dissonance can occur between the Agile team and their suppliers and stakeholders. The very role of an Agile manager here is to plan ahead for these external groups to not act in an Agile manner and prepare for working the delays that this causes into the team's workflow. This is normally achieved by working specific expectations into the contracts.
Risk & Investment Management
As far as staying Agile and developing well goes, the key thing an Agile manager should be looking at is value. Not so much have we exceeded our budget? but what should we be investing in now?. A difference in thinking is needed to achieve this: instead of concentrating on sticking to a once-set plan, the job of the manager is to focus on the best value achievable at the time.
This can only be done by frequent evaluation of the ongoing projects and hence — by working in short iterations. Again, using Agile metrics is of great help in this aspect. An outside perspective to the workflow view is also needed in order to assess possible risks for the ongoing and planned projects.
The Crown Jewel - Change Management
Change management is the one aspect of running an Agile workflow that is better done by one person looking at the whole environment, rather than by teams. This is also when an Agile manager can really shine, as preparing the team to adjust to new demands is key to maintaining the Agile spirit.
A big part of this is also knowing which steps can and cannot be taken while thinking of making a change. It's mostly about balance between what can and should be achieved in a given time and what will simply block the flow, the productivity and the — key here — team's level of satisfaction.
To sum up — it's very tempting to think that self-organizing teams need no management at all. But there are too many facets to running business in any way (Agile or traditional) that need careful looking at and direct management. There are too many jobs that will just not get into place of their own accord.
Mind you, it's clear to see that whereas the job of an Agile manager is similar to a traditional project manager's, there is far less to be managed in an Agile environment, than in the traditional ones.