A solution would be to use temporary variables:
select
@prev as previous,
e.id,
@prev := e.value as current
from
(
select
@prev := null
) as i,
example as e
order by
e.id
To get the "next" value, repeat the procedure. Here is an example:
select
id, previous, current, next
from
(
select
@next as next,
@next := current as current,
previous,
id
from
(
select @next := null
) as init,
(
select
@prev as previous,
@prev := e.value as current,
e.id
from
(
select @prev := null
) as init,
example as e
order by e.id
) as a
order by
a.id desc
) as b
order by
id
Check the example on SQL Fiddle
May be overkill, but it may help you