If you are using SQL Server, you can use the GETDATE() function. This returns the current date/time. If your date-time fields only contain a DATE part, you will need to strip the time part of the result of GETDATE().
SELECT
*
FROM
eventdetails
WHERE
eve_date>=CAST(FLOOR(CAST(GETDATE() AS FLOAT)) AS DATETIME);
You will see that the time part is stripped of the result of GETDATE() by casting it to float, flooring it and casting it back to DATETIME type. There are other ways of doing this, cf Damien's solution. Since DATETIME under the hood is stored as a FLOAT, only one trivial function is called (FLOOR), and performs better than the DATEADD/DATEDIFF trick.
If the eve_date can also contain a TIME part, and you want to compare only the DATE part, you will also have to CAST/CONVERT the eve_date to make the comparison:
SELECT
*
FROM
eventdetails
WHERE
CAST(FLOOR(CAST(eve_date AS FLOAT)) AS DATETIME)>=CAST(FLOOR(CAST(GETDATE() AS FLOAT)) AS DATETIME);
Now this is all written in the perspective of SQL Server 2005 and below, where a DATE type does not exist. For SQL Server 2008 and above, casting to the DATE type will strip the TIME part away as well:
SELECT
*
FROM
eventdetails
WHERE
CAST(eve_date AS DATE)>=CAST(GETDATE() AS DATE);
Note that the GETDATE function is the equivalent of CURRENT_TIMESTAMP function as defined by ANSI SQL standard.