The fastest MySQL solution, without inner queries and without GROUP BY:

SELECT m.*                    -- get the row that contains the max value
FROM topten m                 -- "m" from "max"
    LEFT JOIN topten b        -- "b" from "bigger"
        ON m.home = b.home    -- match "max" row with "bigger" row by `home`
        AND m.datetime < b.datetime           -- want "bigger" than "max"
WHERE b.datetime IS NULL      -- keep only if there is no bigger than max

Explanation:

Join the table with itself using the home column. The use of LEFT JOIN ensures all the rows from table m appear in the result set. Those that don't have a match in table b will have NULLs for the columns of b.

The other condition on the JOIN asks to match only the rows from b that have bigger value on the datetime column than the row from m.

Using the data posted in the question, the LEFT JOIN will produce this pairs:

+------------------------------------------+--------------------------------+
|              the row from `m`            |    the matching row from `b`   |
|------------------------------------------|--------------------------------|
| id  home  datetime     player   resource | id    home   datetime      ... |
|----|-----|------------|--------|---------|------|------|------------|-----|
| 1  | 10  | 04/03/2009 | john   | 399     | NULL | NULL | NULL       | ... | *
| 2  | 11  | 04/03/2009 | juliet | 244     | NULL | NULL | NULL       | ... | *
| 5  | 12  | 04/03/2009 | borat  | 555     | NULL | NULL | NULL       | ... | *
| 3  | 10  | 03/03/2009 | john   | 300     | 1    | 10   | 04/03/2009 | ... |
| 4  | 11  | 03/03/2009 | juliet | 200     | 2    | 11   | 04/03/2009 | ... |
| 6  | 12  | 03/03/2009 | borat  | 500     | 5    | 12   | 04/03/2009 | ... |
| 7  | 13  | 24/12/2008 | borat  | 600     | 8    | 13   | 01/01/2009 | ... |
| 8  | 13  | 01/01/2009 | borat  | 700     | NULL | NULL | NULL       | ... | *
+------------------------------------------+--------------------------------+

Finally, the WHERE clause keeps only the pairs that have NULLs in the columns of b (they are marked with * in the table above); this means, due to the second condition from the JOIN clause, the row selected from m has the biggest value in column datetime.

Read the SQL Antipatterns: Avoiding the Pitfalls of Database Programming book for other SQL tips.

You are so close! All you need to do is select BOTH the home and its max date time, then join back to the topten table on BOTH fields:

SELECT tt.*
FROM topten tt
INNER JOIN
    (SELECT home, MAX(datetime) AS MaxDateTime
    FROM topten
    GROUP BY home) groupedtt 
ON tt.home = groupedtt.home 
AND tt.datetime = groupedtt.MaxDateTime

Another way to gt the most recent row per group using a sub query which basically calculates a rank for each row per group and then filter out your most recent rows as with rank = 1

select a.*
from topten a
where (
  select count(*)
  from topten b
  where a.home = b.home
  and a.`datetime` < b.`datetime`
) +1 = 1

DEMO

Here is the visual demo for rank no for each row for better understanding

By reading some comments what about if there are two rows which have same 'home' and 'datetime' field values?

Above query will fail and will return more than 1 rows for above situation. To cover up this situation there will be a need of another criteria/parameter/column to decide which row should be taken which falls in above situation. By viewing sample data set i assume there is a primary key column id which should be set to auto increment. So we can use this column to pick the most recent row by tweaking same query with the help of CASE statement like

select a.*
from topten a
where (
  select count(*)
  from topten b
  where a.home = b.home
  and  case 
       when a.`datetime` = b.`datetime`
       then a.id < b.id
       else a.`datetime` < b.`datetime`
       end
) + 1 = 1

DEMO

Above query will pick the row with highest id among the same datetime values

visual demo for rank no for each row

@Michae The accepted answer will working fine in most of the cases but it fail for one for as below.

In case if there were 2 rows having HomeID and Datetime same the query will return both rows, not distinct HomeID as required, for that add Distinct in query as below.

SELECT DISTINCT tt.home  , tt.MaxDateTime
FROM topten tt
INNER JOIN
    (SELECT home, MAX(datetime) AS MaxDateTime
    FROM topten
    GROUP BY home) groupedtt 
ON tt.home = groupedtt.home 
AND tt.datetime = groupedtt.MaxDateTime

this is the query you need:

 SELECT b.id, a.home,b.[datetime],b.player,a.resource FROM
 (SELECT home,MAX(resource) AS resource FROM tbl_1 GROUP BY home) AS a

 LEFT JOIN

 (SELECT id,home,[datetime],player,resource FROM tbl_1) AS b
 ON  a.resource = b.resource WHERE a.home =b.home;

I think this will give you the desired result:

SELECT   home, MAX(datetime)
FROM     my_table
GROUP BY home

BUT if you need other columns as well, just make a join with the original table (check Michael La Voie answer)

Best regards.

Why not using: SELECT home, MAX(datetime) AS MaxDateTime,player,resource FROM topten GROUP BY home Did I miss something?

You can also try this one and for large tables query performance will be better. It works when there no more than two records for each home and their dates are different. Better general MySQL query is one from Michael La Voie above.

SELECT t1.id, t1.home, t1.date, t1.player, t1.resource
FROM   t_scores_1 t1 
INNER JOIN t_scores_1 t2
   ON t1.home = t2.home
WHERE t1.date > t2.date

Or in case of Postgres or those dbs that provide analytic functions try

SELECT t.* FROM 
(SELECT t1.id, t1.home, t1.date, t1.player, t1.resource
  , row_number() over (partition by t1.home order by t1.date desc) rw
 FROM   topten t1 
 INNER JOIN topten t2
   ON t1.home = t2.home
 WHERE t1.date > t2.date 
) t
WHERE t.rw = 1

Here is MySQL version which prints only one entry where there are duplicates MAX(datetime) in a group.

You could test here http://www.sqlfiddle.com/#!2/0a4ae/1

Sample Data

mysql> SELECT * from topten;
+------+------+---------------------+--------+----------+
| id   | home | datetime            | player | resource |
+------+------+---------------------+--------+----------+
|    1 |   10 | 2009-04-03 00:00:00 | john   |      399 |
|    2 |   11 | 2009-04-03 00:00:00 | juliet |      244 |
|    3 |   10 | 2009-03-03 00:00:00 | john   |      300 |
|    4 |   11 | 2009-03-03 00:00:00 | juliet |      200 |
|    5 |   12 | 2009-04-03 00:00:00 | borat  |      555 |
|    6 |   12 | 2009-03-03 00:00:00 | borat  |      500 |
|    7 |   13 | 2008-12-24 00:00:00 | borat  |      600 |
|    8 |   13 | 2009-01-01 00:00:00 | borat  |      700 |
|    9 |   10 | 2009-04-03 00:00:00 | borat  |      700 |
|   10 |   11 | 2009-04-03 00:00:00 | borat  |      700 |
|   12 |   12 | 2009-04-03 00:00:00 | borat  |      700 |
+------+------+---------------------+--------+----------+

MySQL Version with User variable

SELECT *
FROM (
    SELECT ord.*,
        IF (@prev_home = ord.home, 0, 1) AS is_first_appear,
        @prev_home := ord.home
    FROM (
        SELECT t1.id, t1.home, t1.player, t1.resource
        FROM topten t1
        INNER JOIN (
            SELECT home, MAX(datetime) AS mx_dt
            FROM topten
            GROUP BY home
          ) x ON t1.home = x.home AND t1.datetime = x.mx_dt
        ORDER BY home
    ) ord, (SELECT @prev_home := 0, @seq := 0) init
) y
WHERE is_first_appear = 1;
+------+------+--------+----------+-----------------+------------------------+
| id   | home | player | resource | is_first_appear | @prev_home := ord.home |
+------+------+--------+----------+-----------------+------------------------+
|    9 |   10 | borat  |      700 |               1 |                     10 |
|   10 |   11 | borat  |      700 |               1 |                     11 |
|   12 |   12 | borat  |      700 |               1 |                     12 |
|    8 |   13 | borat  |      700 |               1 |                     13 |
+------+------+--------+----------+-----------------+------------------------+
4 rows in set (0.00 sec)

Accepted Answers' outout

SELECT tt.*
FROM topten tt
INNER JOIN
    (
    SELECT home, MAX(datetime) AS MaxDateTime
    FROM topten
    GROUP BY home
) groupedtt ON tt.home = groupedtt.home AND tt.datetime = groupedtt.MaxDateTime
+------+------+---------------------+--------+----------+
| id   | home | datetime            | player | resource |
+------+------+---------------------+--------+----------+
|    1 |   10 | 2009-04-03 00:00:00 | john   |      399 |
|    2 |   11 | 2009-04-03 00:00:00 | juliet |      244 |
|    5 |   12 | 2009-04-03 00:00:00 | borat  |      555 |
|    8 |   13 | 2009-01-01 00:00:00 | borat  |      700 |
|    9 |   10 | 2009-04-03 00:00:00 | borat  |      700 |
|   10 |   11 | 2009-04-03 00:00:00 | borat  |      700 |
|   12 |   12 | 2009-04-03 00:00:00 | borat  |      700 |
+------+------+---------------------+--------+----------+
7 rows in set (0.00 sec)

Try this for SQL Server:

WITH cte AS (
   SELECT home, MAX(year) AS year FROM Table1 GROUP BY home
)
SELECT * FROM Table1 a INNER JOIN cte ON a.home = cte.home AND a.year = cte.year

SELECT c1, c2, c3, c4, c5 FROM table1 WHERE c3 = (select max(c3) from table)

SELECT * FROM table1 WHERE c3 = (select max(c3) from table1)

Since people seem to keep running into this thread (comment date ranges from 1.5 year) isn't this much simpler:

SELECT * FROM (SELECT * FROM topten ORDER BY datetime DESC) tmp GROUP BY home

No aggregation functions needed...

Cheers.

SELECT  tt.*
FROM    TestTable tt 
INNER JOIN 
        (
        SELECT  coord, MAX(datetime) AS MaxDateTime 
        FROM    rapsa 
        GROUP BY
                krd 
        ) groupedtt
ON      tt.coord = groupedtt.coord
        AND tt.datetime = groupedtt.MaxDateTime

This will work even if you have two or more rows for each home with equal DATETIME's:

SELECT id, home, datetime, player, resource
FROM   (
       SELECT (
              SELECT  id
              FROM    topten ti
              WHERE   ti.home = t1.home
              ORDER BY
                      ti.datetime DESC
              LIMIT 1
              ) lid
       FROM   (
              SELECT  DISTINCT home
              FROM    topten
              ) t1
       ) ro, topten t2
WHERE  t2.id = ro.lid

Here goes T-SQL version:

-- Test data
DECLARE @TestTable TABLE (id INT, home INT, date DATETIME, 
  player VARCHAR(20), resource INT)
INSERT INTO @TestTable
SELECT 1, 10, '2009-03-04', 'john', 399 UNION
SELECT 2, 11, '2009-03-04', 'juliet', 244 UNION
SELECT 5, 12, '2009-03-04', 'borat', 555 UNION
SELECT 3, 10, '2009-03-03', 'john', 300 UNION
SELECT 4, 11, '2009-03-03', 'juliet', 200 UNION
SELECT 6, 12, '2009-03-03', 'borat', 500 UNION
SELECT 7, 13, '2008-12-24', 'borat', 600 UNION
SELECT 8, 13, '2009-01-01', 'borat', 700

-- Answer
SELECT id, home, date, player, resource 
FROM (SELECT id, home, date, player, resource, 
    RANK() OVER (PARTITION BY home ORDER BY date DESC) N
    FROM @TestTable
)M WHERE N = 1

-- and if you really want only home with max date
SELECT T.id, T.home, T.date, T.player, T.resource 
    FROM @TestTable T
INNER JOIN 
(   SELECT TI.id, TI.home, TI.date, 
        RANK() OVER (PARTITION BY TI.home ORDER BY TI.date) N
    FROM @TestTable TI
    WHERE TI.date IN (SELECT MAX(TM.date) FROM @TestTable TM)
)TJ ON TJ.N = 1 AND T.id = TJ.id

EDIT
Unfortunately, there are no RANK() OVER function in MySQL.
But it can be emulated, see Emulating Analytic (AKA Ranking) Functions with MySQL.
So this is MySQL version:

SELECT id, home, date, player, resource 
FROM TestTable AS t1 
WHERE 
    (SELECT COUNT(*) 
            FROM TestTable AS t2 
            WHERE t2.home = t1.home AND t2.date > t1.date
    ) = 0

This works on Oracle:

with table_max as(
  select id
       , home
       , datetime
       , player
       , resource
       , max(home) over (partition by home) maxhome
    from table  
)
select id
     , home
     , datetime
     , player
     , resource
  from table_max
 where home = maxhome

Try this

select * from mytable a join
(select home, max(datetime) datetime
from mytable
group by home) b
 on a.home = b.home and a.datetime = b.datetime

Regards K