While I often seem to be in the role of firefighter, it is one I despise. The more the firefighter saves the day, the more people play with matches in the gasoline refinery.
I've seen it go both ways. In some cases people come to rely on this person's intervention, but in others it's seen as a badge of failure to have to call in the "firefighter". I think it all comes down to how management handles the situation, as well as the dynamics of the group itself.