Attention! See Update3 for new iTerm versions (works for 2.1.5)
Original Answer
This command allows iTerm to work over fullscreen apps
defaults write ~/Applications/iTerm.app/Contents/Info LSUIElement true
But it hides iTerm’s context menu. To access iTerm’s preferences, right-click on the tabs bar and select the proper menu item; or focus on any iTerm’s window and press ⌘–,.
Update
If you use the beta version of iTerm, there is no need to run the previous command. You can turn on Preferences > Advanced > Hide iTerm2 from the dock and from the ⌘–Tab app switcher.
Also make sure that the profile you use for the dropdown window (Hotkey window by default) is allowed on all spaces (Preferences > Profiles > “Hotkey window” profile > “Window” tab > Space: “all spaces”).
Remember to restart iTerm2.
Update 2
If you can’t find Preferences, use the shortcut ⌘–i or Right Click in an open iTerm2 terminal window, then select “Edit Session”.
Update 3
In 2.1.5, you should use the “Exclude from Dock and ⌘-Tab Application Switcher” option in Preferences -> Appearance. When iTerm2 is excluded from the dock, you can always get back to the Preferences window using the status bar item, or ⌘–,. Look for an iTerm2 icon on the right side of your menu bar.
Update 4
In v.3.4.15, you should follow the comment from @Sudhi. Profiles -> specific Profile -> Keys -> “A hotkey opens dedicated window with this profile” and configure hotkey.