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Apart from other reviews I show you an alternative how you can make this really short with LINQ and Regex:

OK, the first solution wasn't perfect. This one will however can do it correctly:

var alphabet = Enumerable.Range(97, 26).Select (i => (char)i + "+");
var pattern = "(" + string.Join("|", alphabet) + ")";

var compressed2 =
    Regex.Matches(str, pattern)
    .Cast<Match>().Select (m => new 
    { 
        Char = m.Groups[1].Value[0], 
        Count = m.Groups[1].Value.Length 
    })
    .Aggregate (string.Empty, (result, nextGroup)  => 
        result.ToString() 
        + nextGroup.Char 
        + (nextGroup.Count > 1 ? nextGroup.Count.ToString() : string.Empty));

For:

var str = "aaabbccdddeezbbb";

the result is:

a3b2c2d3e2zb3

• First get letter groups with regex and their legths
• Then aggregate them to the final string