None of the services supporting IMAP are free.
OK, I will describe what I actually need. I don't use any email client and I don't want any software to download mails to my computer automatically. I just need a utility that would check my mailbox and alert me if there is any new mail. Once I get an alert, I will login manually to check my mail. Just like it happens while you are logged in yahoo messenger; you get a message "You have 1 new mail" without actually downloading the mail. Something similar that would work with other email addresses. Any such s/w?