CASE statement multiple conditions I've got a simple table below, 

Select * from message_log where  Message = 'BUILD' order by 1;

+------------+-------------+
|  **Message |     Log**   |
+------------+-------------+
|    Build   |  Day Start  |
+------------+-------------+
|    Build   |  Day End    |
+------------+-------------+
|    Build   |  Dusk Start |
+------------+-------------+
|    Build   |  Dusk End   |
+------------+-------------+
|    Build   |  Night Start|
+------------+-------------+
|    Build   |  Night End  |
+------------+-------------+


If I for example write a CASE statement 

SELECT DISTINCT CASE WHEN (Log = 'Day Start') THEN 'RUNNING' END AS A
from message_log where  Message = 'BUILD' order by 1;


It'll return a Null value and a 'RUNNING' value, can I write this in such a way that it doesn't include the null row?
Just add a WHERE condition.  And if you are only displaying one value, RUNNING, then there is no reason for a CASE. Otherwise you will want to evaluate each condition in the CASE including what should display in the event none of the conditions is met; a default value.

So here is the code to your original question:

SELECT 'RUNNING' AS A
from message_log 
where  Message = 'BUILD' 
    AND Log = 'Day Start'
order by 1;


And here is the code for a multi-condition CASE:

SELECT CASE 
    WHEN (Log = 'Day Start') THEN 'RUNNING' 
    WHEN (Log = 'Day End')   THEN 'NOT RUNNING'
    ELSE 'UNKNOWN' END AS A
from message_log 
    where  Message = 'BUILD' 
order by 1;