Get records between date for example in mysql

2009-08-11 to current date

2009-08-11 is to retrieve all date , this is just an example

I have tried WHERE time between date(time) and DATE(time) = CURDATE();

A lot of it depends on the data type for the field you are storing the date ( DATE, TIME, DATETIME, TIMESTAMP, or YEAR) in. You need to make the data you are searching against look like the data type.
Try this:

where table.date_field >= starting_date and <= CURDATE();

Or this if the field is a timestamp data type:

where table.datetime_field >= starting_datetime and <= NOW();

And use your fields holding the datring_date and the field in the table to check agianst. Make sure that the data type is

Why couldn't we use between keyword?
Like, where (table.date_field Between starting_date and CURDATE();

If you want to take out the time component, use date function.

E.g. where date(tbl.datefield) >= date(:dateparam)