I went to C++ from PHP like you, but I was more interested in 3D games and such. Now I have moved on to C# and find it much more enjoyable than C++.
As for your specific areas of interest however, C++ is certainly an option but C# may be better.
Mobile programming with C++ is probably not a good idea. I know it's possible with NDKs and such but for a beginner it's probably not so good. For iPhone development, other than the official SDK, the next best option is the (commercial) MonoTouch framework from Novell. However, you may still need a mac to deploy (I don't know). In terms of Android, if you don't want to touch Java (don't blame you) I believe a C# framework (similar to MonoTouch) is in development and other languages may be available. Other platforms? No idea.
Small desktop apps is also very possible with C++. Assuming you're running Windows, you can use the Win32 API (pain) or the C++/CLI API (better). You could also use a different GUI framework like Qt, wxWidgets or GTK+ which are all also supported on other platforms. Again coming back to C#, GUI development using GTK# in MonoDevelop is so much fun. Having used WinForms in Visual C# Express back in my Windows days, I can say that I now enjoy the process whereas I didn't before.
Games are my main area of interest and the reason I originally picked up C++. Seeing as you've said small and desktop-based, using C++ for performance reasons is way overkill IMO. You could make a decent, fun, playable game in Python using pygame without the pain of using a language like C++. In C# (yes, I'm trying to sell it to you) you could create awesome games using the XNA framework from Microsoft or other frameworks like (my personal favorite) OpenTK.
Rich internet applications. C++ is probably not the right tool to use here. It's certainly possible but seeing as C++ has no standard networking library, you would have to figure some of this stuff out yourself. C# may not be the right tool either but it makes it a little easier. There are other options as well (like Python) but it's not something I know much about.
Despite what I've said about it, I still think C++ is a good language to learn. It teaches you about lower-level things you never think about in PHP land. If you want to learn it, the book that really helped me was "C++: A beginners guide" by Herbert Schildt and also "Programming" by Bjarne Stroustrup.