You were joining your grouped results with the original table with duplicates. You can get an even simpler version of your code like this, no need of a subquery:

SELECT @MSGOUT = @MSGOUT + '

<tr>

<td>' + ServerName +'</td>

<td>' + DBName +'</td>

<td>' + cast(COUNT(dbname) as varchar(5)) +'</td>

</tr>

'

FROM DBINVENTORY

GROUP BY ServerName,DBName

HAVING ( COUNT(DBName) > 1 )