Is it possible not to attach any Master page to your aspx file(s) inside SharePoint Designer 2007?
Sure. You can simply, in Sharepoint Designer, create a blank page. In SPD 2007, just go to File>New>Page, and a panel will appear. Just pick "ASPX" or "HTML".
In SPD 2010, the option is there in the "File" Tab under "File" - you can choose HTML or ASPX, etc. Now, this will create a page that is entirely blank, that is, with no master page or code or anything. You will have to create it in a document library, or some other folder or subfolder of your site.
If you create it in the "Site Assets" or "Site Pages" document library of your root site, (or any folder, really) you can use it pretty much anywhere in your website. You can enter advanced edit mode for the page, and Sharepoint Designer will show you the basic aspx markup - WITH NO MASTER PAGE attached. Then you will see the form tags, too.
If you later decide you want a master page attached to it, make sure your page is in edit mode in Sharepoint Designer, go to Format>Master Page>Attach Master Page.
In SPD 2010, go to the "Style" tab, and click on "Attach", whence you may choose whatever master page you like. If it complains that the content tags don't match, just click "Okay" and the page will be reformatted to match the newly chosen master page. As long as you haven't added content to the content containers, you shouldn't have any problems (I'm not sure what will happen if you have created a complicated page; if you only have simple html text, I have found that it gets converted without much issue.).
If you put the page in the document library at root and left it with the default name, you can browse to it at http://my.portal.com/untitled_1.aspx