How to group by DESC order

Normally MySQL allows group by ascending order records only. So we can order records before grouping.

SELECT *
FROM (
  SELECT *
  FROM questions
  ORDER BY id DESC
) AS questions
GROUP BY questions.asker

The records need to be grouped using GROUP BY and MAX() to get the maximum ID for every asker.

SELECT  asker, MAX(ID) ID
FROM    TableName
GROUP   BY asker

• SQLFiddle Demo

OUTPUT

╔════════╦════╗
║ ASKER  ║ ID ║
╠════════╬════╣
║ Bob    ║  2 ║
║ Marley ║  3 ║
╚════════╩════╝

If you want the last id for each asker, then you should use an aggregate function:

SELECT max(id) as id, 
   asker
FROM questions 
GROUP by asker 
ORDER by id DESC

The reason why you were getting the unusual result is because MySQL uses an extension to GROUP BY which allows items in a select list to be nonaggregated and not included in the GROUP BY clause. This however can lead to unexpected results because MySQL can choose the values that are returned. (See MySQL Extensions to GROUP BY)

From the MySQL Docs:

MySQL extends the use of GROUP BY so that the select list can refer to nonaggregated columns not named in the GROUP BY clause. ... You can use this feature to get better performance by avoiding unnecessary column sorting and grouping. However, this is useful primarily when all values in each nonaggregated column not named in the GROUP BY are the same for each group. The server is free to choose any value from each group, so unless they are the same, the values chosen are indeterminate. Furthermore, the selection of values from each group cannot be influenced by adding an ORDER BY clause. Sorting of the result set occurs after values have been chosen, and ORDER BY does not affect which values the server chooses.

Now if you had other columns that you need to return from the table, but don't want to add them to the GROUP BY due to the inconsistent results that you could get, then you could use a subquery to do so. (Demo)

select 
  q.Id,
  q.asker,
  q.other -- add other columns here
from questions q
inner join
(
  -- get your values from the group by
  SELECT max(id) as id, 
    asker
  FROM questions 
  GROUP by asker 
) m
  on q.id = m.id
order by q.id desc