It seems like most of common web browsers (Firefox, Chrome, Safari) are developed using C++. Whys is that so?
Another way to ask the question is what kind of support does a browser need?  The short list is:


Support for parsing (needed to make sense of [X]HTML, CSS, and [ECMA/Java]Script)
Tree walking/interpreting features (part of parsing and building UI)
Support for accelerated graphics
Fast networking
For the more advanced browsers: control over processes and isolating memory between pages
Must work on all supported platforms


Most languages have some sort of parsing support.  You have parser generators for C, C++, C#, Java, etc.  However, C and C++ have quite a few years head start on the rest of the alternatives so the algorithms and implementations are more mature.  Accessing accelerated graphics in Java is a no go, unless you have some native extensions to make it work.  WPF on C# provides access to accelerated graphics, but it is too new to have a serious browser built with the technology.

Networking is actually the least of the reasons to choose C++ over Java or C#.  The reason is that communication is many times slower than the rest of the processing that goes on to display the page.  The raw speed of the wire is the limiting factor.  Both Java and C# have non-blocking IO support, as does C++.  So there really is no clear winner in this area.

Why not Java?
Have you ever tried to build a UI with Java?  It feels cumbersome and slow compared to anything else out there, because it is.  No accelerated graphics is also a big negative here.  Java's sandboxing is really good, and can help improve the security of a browser if it is used correctly, but it is a pain to configure and make work.  Not to mention the graphics format support lags behind most modern browsers.

Why not C#?
If your only target is Windows, C# might actually make a good
representation.  The problem comes when you want to support anything else.  Mono hasn't caught up enough to be considered cross platform enough for this task--particularly with accelerated graphics support and WPF.  Who knows how long that will take to change.

Why not C?
There's a C compiler for just about every platform out there (including embedded devices).  However, there's a lot that C does not do for you that you will have to be extra vigilant about.  You have access to all the lowest levels of the APIs, but the majority of C developers don't do GUIs.  Even the C GUI libraries are written in an object oriented manner.  As soon as you start talking UI, an object oriented language starts making better sense.

Why not Objective C?
If your only target is Apple, it makes a lot of sense.  However, most developers don't know Objective-C, and the only reason to learn it is to work on NeXT or Apple boxes.  Sure you can use any C library with Objective-C, and there are compilers for many platforms, but finding people to work on it will be a touch more difficult.  Who knows?  Maybe Apple can turn this perceived deficiency around.

Why C++?
There's a C++ compiler for just about every platform out there.  Almost every GUI library has a C++ interface, sometimes it's better and sometimes it's just different.  For example, Microsoft's ATL is a lot better than win32 C function calls or even the MFC library.  There's C++ wrappers for GTK on Unix, and I'd be surprised if someone didn't have a C++ wrapper around Apple's Objective-C GUI library.  Process management is easier within C++ than Java or C# (those details are abstracted away for you).  It's perceived speed comes more from hardware acceleration than it does raw performance.  C++ does take care of more things for you than raw C (such as bounded strings), but still gives you freedom to tweak things.  Not to mention a number of libraries needed to render web pages are also written in C or C++.

For the time being, C++ does edge out the alternatives.
