Max from 2 columns with priority date col then the seq col Oracle
You don't mention DBMS, so I'll assume it is one that supports window functions (DB2, Oracle, SQL-server, Postgres, etc)

select personid, xdate, seqnumber
from (
     select personid, xdate, seqnumber
          , row_number() over (partition by personid
                               order by xdate desc, seqnumber desc) as rn
     from T
) as X
where rn = 1;


Edit: added sample data and result (http://sqlfiddle.com/#!4/73ad2/4)

create table T
(   personid   int
,  xdate      date
,  seqnumber  int );

ALTER SESSION SET NLS_DATE_FORMAT = 'YYYY-MM-DD';

insert into t values (123, '2012-01-01', 0);
insert into t values (123, '2011-01-01', 0);
insert into t values (136, '2012-01-02', 1);
insert into t values (136, '2012-01-02', 0);
insert into t values (136, '2012-01-01', 0);
insert into t values (168, '2012-01-04', 2);
insert into t values (168, '2012-01-04', 1);
insert into t values (168, '2012-01-04', 0);

select personid, xdate, seqnumber
from (
    select personid, xdate, seqnumber
         , row_number() over (partition by personid
                              order by xdate desc, seqnumber desc) as rn
    from T
) x
where rn = 1;

PERSONID    XDATE   SEQNUMBER
123     January, 01 2012 00:00:00+0000  0
136     January, 02 2012 00:00:00+0000  1
168     January, 04 2012 00:00:00+0000  2