这里有一个简单的解决方案：

private static string RemoveDuplicates(string str)
    {
        // Sample: "AAbcdd445h" > "Abcd45h"
        if (string.IsNullOrEmpty(str))
        {
            return string.Empty;
        }
        if (str.Length == 1)
        {
            return str.Substring(0, 1);
        }
        var sb = new StringBuilder();
        int index = 0;
        while (index < str.Length - 1)
        {
            if (str[index] == str[index + 1])
            {
                // Current char is the same with next one, take it and jump 2 chars.
                sb.Append(str[index]);
                index += 2;
            }
            else
            {
                // Current char is different from the next, take it and pass to next.
                sb.Append(str[index]);
                index++;
            }
            // Check the last character
            if (index == str.Length - 1)
            {
                sb.Append(str[index]);
            }
        }
        return sb.ToString();
    }

样品：
如果：
输入：aaabbbcccaaabbbccc
输出：abc

static void Main(string[] args)
    {
        HashSet<char> tmpSet = new HashSet<char>();

        string input = "aaabbbccc";

        foreach(char c in input.ToCharArray())
        {
            tmpSet.Add(c);
        }

        string final = string.Join("", tmpSet);

        Console.WriteLine("Result : " + final);
    }

输出：
结果：abc
如果：
输入：aaabbbcccaaabbbccc
输出：abcabc

static void Main(string[] args)
    {
        string input = "aaabbbcccaaabbbccc";
        string final = "";

        if (input.Length > 0)
        {
            final += input.Substring(0, 1);

            for(int i = 1; i < input.Length; i++)
            {
                string strValue = input.Substring(i, 1);
                if (final.Substring(final.Length - 1, 1) != strValue)
                {
                    final += strValue;
                }
            }
        }

        Console.WriteLine("Result : " + final);
    }

输出：
abc