C#: How would you make a unique filename by adding a number?

Question

I would like to create a method which takes either a filename as a string or a FileInfo and adds an incremented number to the filename if the file

Answer 1

public FileInfo MakeUnique(string path)
{            
    string dir = Path.GetDirectoryName(path);
    string fileName = Path.GetFileNameWithoutExtension(path);
    string fileExt = Path.GetExtension(path);

    for (int i = 1; ;++i) {
        if (!File.Exists(path))
            return new FileInfo(path);

        path = Path.Combine(dir, fileName + " " + i + fileExt);
    }
}

Obviously, this is vulnerable to race conditions as noted in other answers.