I always have my IDE (phpStorm) in full screen mode (Yosemite).

I want my iTerm2 hotkey to slide my terminal window down over the IDE, so it doesn't open up a new space for the terminal window. As once the window slides back up it leaves me on an empty space, rather than going back to phpStorm.

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.