There is a library on NuGet called ExifReader and an accompanying CodeProject article here.
The following code should work for getting the orientation, and you can use the other enumerations of ExifTags to get other pieces of metadata:
object result;
var reader = new ExifReader("c:\\temp\\test\\sample.jpg");
reader.GetTagValue(ExifTags.Orientation, out result);
var orientation = Convert.ToInt32(result);
I have tested this with this image on Windows XP 32-Bit SP3 using .Net 4, and it returned an orientation of 1, which appears to be correct.