Too many windows open on my screen...

Use Mission Control to add some desktops. Move related apps to single desktops, like Mail, Contacts, Calendar (maybe).

http://support.apple.com/kb/HT4689

http://support.apple.com/kb/PH10565

http://support.apple.com/kb/PH11353

http://support.apple.com/kb/PH10565

http://support.apple.com/kb/PH11318

You can still drag and drop between desktops.

Here is a tutorial on Exposé: http://support.apple.com/kb/VI22

I don't know if there is any info in those of dragging, but you can start dragging, then invoke Mission Control, or App Switcher (cmd-tab), to move to the destination app. Hover over the App windows and it will outline, then pop up to be active. You can then drop in that window.

Try staggering your applications and shrink the window size by pushing up and to the left from the bottom right hand corner of the window. To change applications, click on it to bring it to the front. Screen shot of a 24" iMac.

Mission Control is spaces.

If you want stuff to go into the background when you drag, start dragging, invoke Exposé, hover over Mail's message window until it comes to the forefront, then drop. You can achieve a similar result by cmd-tabbing to Mail while you are dragging.

For your example, use Mission Control to show the Desktop only, grab the file and start dragging, then use Mission Control or the App Switcher to move to Mail. Hover until active, then drop.

Or, if you haven't started composing an email, drop the file onto the Mail icon in the Dock.

You can have spaces (now called desktops) by adding new desktops and assigning applications to a specific desktop. I have 4 desktops - see screen shot.

Mission Control – Work in Multiple Spaces

1. If you want to keep the desktops in a specific order, go to System Preferences/Mission Control and uncheck the box " Automatically rearrange spaces based on most recent use." You can also select the box below that so if you open an application, you'll be taken to that space.
2. If you want to cut down the number of desktops, there is also an option to remove the Dashboard as a desktop and have it work like it did in Snow Leopard. That can be set in System Preferences/Mission Control by deselecting Show Dashboard as a space. You can access the Dashboard by clicking on the Dashboard icon in the dock or using the FN 12 key.

You are welcome.