Airports do have areas where photography isn't permitted, but I've travelled quite a bit and I haven't come across any restrictions on carrying a camera in your hand luggage or over your shoulder. I suppose there may be some exceptions, but they're probably not places where most people choose to go. Some African countries I've visited do tend to make up the rules as they go along, but I'd be more worried about attracting unwanted attention than contravening the "regulations" by carrying anything openly that's obviously valuable.
Airlines have their own regulations, and can be more or less flexible/inflexible about them. If you're in any doubt, assume they'll be inflexible.