mysql.sql

select
  yearweek(field, 1)
from
  table;

postgres.sql

select
  EXTRACT(isoyear from field)*100 + EXTRACT(week from field - (EXTRACT(dow FROM field)::int+6)%7)
from
  table;

sqlite.sql

select
  case
  when strftime('%W', strftime('%Y-01-04', field)) = '00' then
    -- 01/01 is in week 1 of the current year => %W == week - 1
    case
    when strftime('%W', field) = '52' and strftime('%W', (strftime('%Y', field) + 1) || '-01-04') = '00' then
      -- we are at the end of the year, and it's the first week of the next year
      (strftime('%Y', field) + 1) || '01'
    when strftime('%W', field) < '08' then
      -- we are in week 1 to 9
      strftime('%Y0', field) || (strftime('%W', field) + 1)
    else
      -- we are in week 10 or later
      strftime('%Y', field) || (strftime('%W', field) + 1)
    end
  else
      -- 01/01 is in week 53 of the last year
      case
      when strftime('%W', field) = '52' and strftime('%W', (strftime('%Y', field) + 1) || '-01-01') = '00' then
        -- we are at the end of the year, and it's the first week of the next year
        (strftime('%Y', field) + 1) || '01'
      when strftime('%W', field) = '00' then
        -- we are in the week belonging to last year
        (strftime('%Y', field) - 1) || '53'
      else
        -- everything is fine
        strftime('%Y%W', field)
      end
  end
from
  table;

Note: this will be part of a group by, not a select and should give 200953 for 2010-01-01 (which is in the 53th week of 2009 per ISO-8601).