Edit: *** DO NOT use Turbo C++ *** That's an ancient compiler that won't ever compile modern standard C++ programs, and the pre-standard dialect that it does support will not compile under any modern compiler.
---- back to the original post:
If you are learning standard C++, the GNU C++ compiler is very good. If you are running Linux, Unix or Mac OSX, you already have it. This has been "ported" (jargon for making a version that runs on another OS) to Windows too. There are a couple of options, but MinGW is easier to set up and produces native Windows code.
One of the nicest and easiest ways to get MinGW is to download the Code::Blocks IDE bundled with MinGW. That gives you a good editor and build tool for both C and C++ projects, and installs the compiler along with the IDE (that's "Integrated Development Environment") with just one installation. Check the download page at:
http://www.codeblocks.org/
If you're running on OSX/Linux/Unix, then you can still use Code::Blocks, but there's no bundled compiler, since you already have it. (Actually, some Linux distros come with GNU C but not GNU C++, so you may have to download something after all.)
Microsoft has a free version of Visual Studio (or just Visual C++ if you must use the 2010 version to run with XP or Vista...the 2012 version combines C/C++/C#/VB, but requires Win7 or later.) It's a high quality compiler, nearly as modern as GCC (but neither has full C++11 support yet) and has very good debugging tools. It's harder for beginners because the templates provided for C and C++ projects are incompatible with standard C and C++ programs. You have to start from an empty project, or (better) carefully customize a console project, in order to get standard programs to compile and run. If you're still interested, go to:
http://www.microsoft.com/visualstudio/eng/products/visual-studio-express-products
...and get the Windows Desktop version for Win7 or later. If you're running XP or Vista, then click the "2010 Express Product" link under Downloads at the bottom of the page, and click on "Visual C++ 2010 Express". Annoyingly, you now have to click the arrow, and then click the tiny "Visual C++ 2010 Express" link that says, effectively, "Yes, I *really* want to use the 2010 version!"
Like I said, Code::Blocks is easier, and it's an environment that you can run under every major OS.
PS: I forgot. The link to MinGW to get it all by itself. If you use another IDE (like Eclipse or NetBeans, but C::B is better for C/C++) then install the compiler first and let the IDE install find the compiler and related tools. That's usually much easier than the other way around.
MinGW: http://mingw.org/
Setup instructions: http://mingw.org/wiki/InstallationHOWTOforMinGW