just to make sure: from your example i assume you or not talking about unix timestamp, right?
from version 4.1.1 there is the DATE() function which "Extracts the date part of the date". it then should be simply
WHERE DATE(timestamp_column) = CURDATE()
with older versions, there may be different approaches. you could try
WHERE timestamp_column BETWEEN CONCAT( CURDATE( ) , '000000' ) AND CONCAT( CURDATE( ) , '235959' )
(this does not look particularly elegant to me, though, and I cannot seem to remember whether BETWEEN is exclusive or inclusive the border values.)
another one:
WHERE timestamp_column BETWEEN CURDATE( ) - INTERVAL 1 SECOND AND CURDATE( ) + INTERVAL 1 DAY
(same doubts about the borders here)
however, there may be a lot more ways which may be more efficiently.
[edit: uh, I didn't mean to use the non-existing DATE() function in the pre-4.1.1 examples. copy&paste error 🙁]