Checking your email address in such sites looks like a great way to collect email addresses
If they have other data on your email address, they don't need your email address to do anything with it. If they don't have other data, then there's no issue.
You're not concerned about people having public access to your twitter handle, why would you be concerned about people having public access to your email address.
It's not like that email addresses are that hard to find when they are listed on websites publically...
ereny*gdir*n[@AT]gm*ilAny site that requires you to provide an email address and password (or any other "verifiable info") to check is probably a scam.
Then again just <firstname><lastname>@(gmail|yahoo|hotmail).com works for a lot of people.