Create Login System without creating Cookies and Sessions

Well, yes, you can...but I would strongly advise against it.
Cookies and Sessions hide info from teh user as well as passing it from page to page. If you don't use either of them, then there is no method to pass data except to use the QueryString which can be appended to the HTTP address of teh page - you've seen them with google links as so forth, I suspect:

https://www.google.co.uk/search?q=QueryString&oq=QueryString&sourceid=chrome&ie=UTF-8

gives the page id:

https://www.google.co.uk/search

followed by a question mark, then a set of parameters joined with ampersand characters:

q=QueryString
oq=QueryString
sourceid=chrome
ie=UTF-8

You can use a similar mechanism yourself, but it does have a fairly high security cost: it is easy to access, copy and paste so it is easy for a fake user to work with. In addition, you have to keep checking if the user info presented is actually valid and genuine every time you load a page to prevent spoofing.

On the whole, I'd stick with session / cookies and the .NET Membership system. It's a lot easier, and more secure that rolling your own from query strings!