remove duplicate rows based on one column value

This is similar to Gordon Linoff's query, but without the subquery:

DELETE t1 FROM table t1
  JOIN table t2
  ON t2.refID = t1.refID
  AND t2.ID < t1.ID

This uses an inner join to only delete rows where there is another row with the same refID but lower ID.

The benefit of avoiding a subquery is being able to utilize an index for the search. This query should perform well with a multi-column index on refID + ID.

I would do:

delete from t where 
ID not in (select min(ID) from table t group by refID having count(*) > 1)
and refID in (select refID from table t group by refID  having count(*) > 1)

criteria is refId is among the duplicates and ID is different from the min(id) from the duplicates. It would work better if refId is indexed

otherwise and provided you can issue multiple times the following query until it does not delete anything

delete from t 
where 
ID in (select max(ID) from table t group by refID  having count(*) > 1) 

In MySQL, you can do this with a join in delete:

delete t
    from table t left join
         (select min(id) as id
          from table t
          group by refId
         ) tokeep
         on t.id = tokeep.id
    where tokeep.id is null;

For each RefId, the subquery calculates the minimum of the id column (presumed to be unique over the whole table). It uses a left join for the match, so anything that doesn't match has a NULL value for tokeep.id. These are the ones that are deleted.

Some another variant, in some cases a bit faster than Marcus and NJ73 answers:

DELETE ourTable 
FROM ourTable JOIN 
 (SELECT ID,targetField 
  FROM ourTable 
  GROUP BY targetField HAVING COUNT(*) > 1) t2 
ON ourTable.targetField = t2.targetField AND ourTable.ID != t2.ID;

Hope that will help someone. On big tables Marcus answer stalls.