Open existing file, append a single line

Choice one! But the first is very simple. The last maybe util for file manipulation:

//Method 1 (I like this)
File.AppendAllLines(
    "FileAppendAllLines.txt", 
    new string[] { "line1", "line2", "line3" });

//Method 2
File.AppendAllText(
    "FileAppendAllText.txt",
    "line1" + Environment.NewLine +
    "line2" + Environment.NewLine +
    "line3" + Environment.NewLine);

//Method 3
using (StreamWriter stream = File.AppendText("FileAppendText.txt"))
{
    stream.WriteLine("line1");
    stream.WriteLine("line2");
    stream.WriteLine("line3");
}

//Method 4
using (StreamWriter stream = new StreamWriter("StreamWriter.txt", true))
{
    stream.WriteLine("line1");
    stream.WriteLine("line2");
    stream.WriteLine("line3");
}

//Method 5
using (StreamWriter stream = new FileInfo("FileInfo.txt").AppendText())
{
    stream.WriteLine("line1");
    stream.WriteLine("line2");
    stream.WriteLine("line3");
}

using (StreamWriter w = File.AppendText("myFile.txt"))
{
  w.WriteLine("hello");
}

Or you could use File.AppendAllLines(string, IEnumerable<string>)

File.AppendAllLines(@"C:\Path\file.txt", new[] { "my text content" });

You can use File.AppendAllText for that:

File.AppendAllText(@"c:\path\file.txt", "text content" + Environment.NewLine);