please try this sqlFiddle
SELECT value,
(SELECT value FROM example e2
WHERE e2.value < e1.value
ORDER BY value DESC LIMIT 1) as previous_value,
(SELECT value FROM example e3
WHERE e3.value > e1.value
ORDER BY value ASC LIMIT 1) as next_value
FROM example e1
WHERE id = 3
Edit: OP mentioned to grab value of previous id and value of next id in one of the comments so the code is here SQLFiddle
SELECT value,
(SELECT value FROM example e2
WHERE e2.id < e1.id
ORDER BY id DESC LIMIT 1) as previous_value,
(SELECT value FROM example e3
WHERE e3.id > e1.id
ORDER BY id ASC LIMIT 1) as next_value
FROM example e1
WHERE id = 3