The BitConverter class has a field IsLittleEndian which, according to the documentation:
Indicates the byte order (\"endianness\") in which data is st
Depends on what you mean by ".Net implementations". I'm not aware of Microsoft .NET Framework version for big-endian platform (but see other answers). But if you mean CLI/CLR implementation, then both Mono and DotGNU have versions for big-endian machines. Mono runs at least on Solaris 10 on Sparc and on Mac OS X on PowerPC. DotGNU has much wider list of available platforms.