Given that for some dates you have no data, you'll need to fill in the gaps. One approach to this is to have a calendar table prefilled with all dates you need, and join against that.
If you want the results to show day numbers as you have showing in your question, you could prepopulate these in your calendar too as labels.
You would join your data table date field to the date field of the calendar table, group by that field, and sum values. You might want to specify limits for the range of dates covered.
So you might have:
CREATE TABLE Calendar (
label varchar,
cal_date date,
primary key ( cal_date )
)
Query:
SELECT
c.label,
SUM( d.values )
FROM
Calendar c
JOIN
Data_table d
ON d.date_field = c.cal_date
WHERE
c.cal_date BETWEEN '2010-01-01' AND '2010-01-31'
GROUP BY
d.date_field
ORDER BY
d.date_field
Update:
I see you have datetimes rather than dates. You could just use the MySQL DATE() function in the join, but that would probably not be optimal. Another approach would be to have start and end times in the Calendar table defining a 'time bucket' for each day.