Having done this a couple of times now for work, I can provide an answer...but you're probably not going to like it. As Nathan mentioned, it depends on the country. It also depends on the work you'll be doing while in country. That's the short version.
If you're traveling with a small amount of your own gear (by that, I mean fits in the suitcase with your clothes)...and plan to carry it back out with you...then you're probably not going to have any customs issues. Once film licenses start getting involved when traveling as part of a crew, things begin to get a bit more complicated. In those instances, it's rare that I haven't had to declare gear on the way in and out, with some form of itemized list, and have it randomly inspected. We've never had to pay import duties in those cases, but there are frequently customs fees that need to be paid (on the way in, way out, or both).
We've always travelled with our gear, but from what I've seen...the shipping option that many people use now ends up very similar. They just don't have to deal with flight-checking gear and customs immediately after long flights. There's always paperwork involved in those cases, and the required paperwork varies based on the nations involved (note the plural!!). Most countries have some sort of customs information available online for film/media crews. They're not always easy to find, and it may be in your interest to contact an embassy/consulate if you're having trouble.
As to your other question, import duties are expected for any purchases made outside of the country they're coming into (provided they're not going back out with the person who brought them in). The U.S. provides a personal allowance (can't remember if it's $500 or $1000) on purchases brought back during travel before they start charging import duties. I don't know if other countries do this or not. If your girlfriend has declared it at some point during the travel, there is a possibility that she'll be checked for it (definitely if she gets pulled for a random screening). If she doesn't have it, she'll need a solid excuse (i.e. physical copy of a police report) or she could get in trouble. I have no idea what those kinds of fines are like.
It's a quagmire to be sure. Hope this helps a little.