Reassign Team Members
It's unlikely that an employee stays his whole life at the company at the same product/project so moving between teams is something which need to be explored and handled.
There is the case that the employee wants to be on a different team. I don't want to cover that in detail since most places worth working for will have a process which makes that relatively painless. In my career I found applying internally for the next higher position to work well - others on blind suggest that sticking to a team to be promoted might be better. So see what works in your place (also don't discount “The Game”)
So we will look at some ways reassignments might work and how they can be tied in with your career.
Boom and bust
This is the predominant model at big places. They stand up a department to explore some business opportunity and if that doesn't work or growth slows lay everyone off and ask them to find a new position. Usually HR encourages internal hires over external ones which gives internal candidates some advantages. However, mostly people with a good rapport and good reputation with the other teams at the company will have an easier time finding something internally. Despite it's Darwinism it's a straight forward way to reassign people. There is also no question if you are managed out - they usually provide resume clinics!
Invited on a new team
Occasionally some manager or even your own manager will approach you and tell you there is an opportunity to join another team permanently. Maybe, it's before your team goes bust, a promotion, or some cooler technology - or something nefarious like putting you on a team which is about to go bust. Just evaluate each opportunity and how it maps to your career - very similar to taking a new position.
The idea is that your team needs something done by another team but they are unable to do that at the timeframe it's needed by your team. So your boss sends you over to add that functionality to unblock your team. The scope is reasonable well defined though I have heard of cases where the new engineer had to fix some unrelated bugs “to get familiar with the code base” - but if you have a good boss that can be worked out to eveyones satisfaction. Once you are done you go back and argue that you are a better engineer because you have been exposed to other aspects of the company and have a broader view. If your place is into recommendation letters from outside the team for a promotion - this is it. If the new team is more cool than the old one you can angle for a transfer. All in all this can work out well or at least inform you how good your manager is if you are still stuck on fixing unrelated bugs after a considerable while.
Some team is doing important work for the company and to accelerate that work they reassign you to the new team to “help out”. In a normal environement I am skeptical about those things since if it's a long term assignment I would expect a reporting change and if it's more temporary I question if people have read the Mythical Man Month
There are exeception (see Help out #2) but let's assume that's how they run their ship. If you work with well trained managers they will give you a spiel how your unique skills are needed at the new team to move the company forward, etc. If they are really good, they will point out that engineers at the next career level need a broad understanding of the company and this is an excellent opportunity for you to have this experience. We should have a natural skepticism about that and see if we can extract some tangible promises.
If they don't give the spiel, there is a real possibility that they are trying to manage people out by assigning less interesting tasks in the hope of people quitting. In fact one manager reassigning people told me that he picked the ones least likely to quit - so it's safe to assume they know…
Making this successful is a challenge as it is with akways having more than one manager. So the real goal is to get moved to report to the person in charge of the managers – which makes this a delicate political exercise.
Help Out #2
You work for the director/VP and he tells you to help some team in his org to get things done faster. If you are at that level you can handle the politics and you might even be the troubleshooter they bring in to close projects. Since you and the manager on that team report to the same guy it's a delicate situation because you can easily make the manager look bad and vice versa - also you wouldn't be sent there to help out if things were going swimmingly. But you are at that level for a reason. You got that.
Know yourself: If you prefer clear reporting structures and goals, “boom and bust” is your thing. “Helping Out” is more a polictical balance act since you need to make your audience the VP. “He, I can add value to any of your teams so I should be a direct report with the appropriate title”.