If you are using an Access database then you should place it on a folder outside of your web site so that it is not accessible through a web browser so that hackers can not download your database.
If you are using SQL srever as the database it could be possible to read in the password using packet sniffing tools as the data is passed across the network, so if you really wanted to be secure you could encrypt the password.
You should be fine with storing passwords in a ASP variable, don't use cookies through.