I'm doing C++ and Visual C++ for a college course, using Borland's C++ Builder.

I'd like to do my home assignments using a C++ environment that is similar to Borland and which will produce source code that works in both Borland and in Linux. Which application would be best suited for this? QT, GTK, Anjuta? Something else?

I use KDevelop. Highly recommend it.

QT and GTK are both toolkits, not environments. They're used for creating GUIs whereas Anjuta is an Integrated Development Environment, which is what I assume you're looking for? (feel free to correct me if I'm wrong)

So, if you're looking for an IDE, I guess it all depends on what you're looking for. If you're planning on running it on Linux, then some that are quite popular are:
- Anjuta
- Kdevelop
- Bluefish
- Eclipse (with the CDT plugin for C/C++)
- VIM/EMACS (traditionally more oriented towards being mostly just text editors, but they're both very featureful and so some would argue that they're complete IDEs)

I'm sure there are probably others, but those are the main ones that come to mind right now. As for which one's the best, there's no such thing! It's really a matter of personal preference and which one fits your needs the best. Try them out and see what you like/dislike. The beauty of freedom is choice

Hope that helps!

Since I completely migrated to Linux (2 years ago), I've tried a lot of IDEs including all of 'Gato Azul' posts and even some others. And except for emacs (which is extreme powerful but very .... "special") I wasn't pleased with any of them. So if you are not willing to learn emacs (or maybe vim), I would highly recommend a quite young project named 'Code::Blocks', which I came across some months ago. You will find it here:
http://www.codeblocks.org/

Although it's still under heavy development and there is no final release so far, you will get a highly customizable and extensible IDE for C++, though it is also very lightweight. The latest builds are quite stable and you (as well as everyone else) should definitely give it a try. But one note: Don't use the version '1.0RC2'! -This one will make you angry. These guys count a little bit different than the rest of the world and than one could expect. They released this version a couple of month ago and it has nothing to do with a "final release candidate": Since that time they added a lot of new features and fixed most of the numerous bugs of that version, so you should go with one of the latest nightly builds:
http://www.codeblocks.org/source_code.shtml

Code::Blocks is Open Source and uses wxWidgets, so it works with Linux as well as Windoze. But as "Gato Azul" mentioned, this is just my favour and at last it is all a matter of personal preference. Try around....