I've recently been hired as an assistant professor and will be starting this fall. As I'm beginning to be included on departmental e-mail and in certain decisions, I'm starting to interact (at least via e-mail) with my colleagues. How should I address them? As a graduate student and postdoc, I've always addressed faculty as Prof. X unless I was already very familiar with them or unless they've told me to do otherwise. Is it strange to continue to do this as a professor? I don't want to be disrespectful, but at the same time it feels a little stuffy to continually refer to everyone as Prof. X until they suggest I do otherwise.
In the US, you generally address colleagues of a similar status by their first names—so your fellow faculty members would definitely be addressed informally. This would of course extend to collaborators and acquaintances in other departments.
I think the only exception to this would be in the case of formal communications—an official memorandum or letter from a faculty member to someone in the university administration, for instance. But otherwise, in any oral or informal written correspondence, I'd stick to first names.
(In other countries, follow the appropriate local traditions, as they may be very different from US standards.)