create file and append it

Your porlbem is that multiple threads or processes are trying to access your fiel at the same time.
You need to call your file using a lock or a mutex:
use lock if your program is multithreaded.
public void WriteLog(string TextStr)
        {
            string FilePath = ConfigurationManager.AppSettings["LogPath"].ToString();
           
            //Set Filename By Date
            string FileName = DateTime.Now.ToString("MM-dd-yyyy") + ".txt";
            string FullName = FilePath + FileName;
           
            //check if file exists, else create one
lock(this)
{
            FileStream fileStream = new FileStream(@FullName, FileMode.Append);
            StreamWriter SW;
            SW = File.AppendText(FullName);
            SW.WriteLine(TextStr);
            SW.Close();
}
        }


else use mutex
http://msdn.microsoft.com/en-us/library/system.threading.mutex.aspx

Alternatives: use Trace class and specify your file, log framework (log4net)
http://stackoverflow.com/questions/1260157/whats-the-most-widely-used-logging-framework-in-c

Another small problem though:
For the new line character I am adding "\\n" to the string, but it is simply writing \n to the file. what do I do to make it write a new line character?

Thanks

When you put two backslashes together it means "interpret this as a single backslash character, not an escape sequance"
So "\\n" = \n
and "\n" = newline
But, you probably want "\r\n" which is the normal line termination sequence in Windows, or you can use Environment.NewLine - e.g. WriteLine("Hello World!" + Environment.NewLine);

I tried both "\r\n" and Environment.NewLine
Both write \n in my text file
see example:
\nMain Method In ResultGenerator\nCaseNo not passed in.\nSystem.IndexOutOfRangeException: Index was outside the bounds of the array.
   at ResultGenerator.ResultGenerator.Main(String[] args) in E:\Projects\ResultGenerator\ResultGenerator.cs:line 20

If you start a string with "@" then no escape sequences are recognized.
e.g.
@"Hello\r\nWorld" = Hello\r\nWorld
"Hello\r\nWorld" = Hello <newline> World
I recommend you use the String.Format method,
string message = String.Format("{0}\r\n{1}\r\n{2}", "Main Method in ResultGen", "CaseNo not passed", ex.Message);

mas_oz2003:
Thanks for pointing me to alternate soultions for logging. Is it a good idea to write to OS event log?
Any disadvantages?