New email message with a global keyboard shortcut
I once found a solution for this over at macrumors.com, that works for me. I will quote the important parts (original post from swiftaw):


Create a service in Automator


Open Automator
Select Service template
On the right hand side, use the pull down menus to make it say "Services receives no input in any application.
From the left hand panel select Mail, then drag "New Mail Message" to the right hand panel. 
Save, give it a name like "New Mail Message"

Create a keyboard shortcut


Open System Preferences
Select Keyboard
Select Keyboard Shortcut
Select Services
Find "New Mail Message" in the list, add keyboard shortcut (I used Shift+Apple+M) by clicking to the right of the name. 

Check that it works. (You can also launch it by clicking on AppName->Services->New Mail Message in the menu bar of any App.
Note, if Mail isn't running, Mail will launch and then create a New Message.


But there is also a built-in solution for composing a new e-mail from anywhere, although it is not a keyboard shortcut: ctrl+click or right click on the Mail.app icon in the doc to get the menu and select Compose New Message. 

 

Also, there are some individual application shortcuts from within the applications like CMD+i from within Safari.