How do I Launch an Applescript with a Hotkey Without Automator?
I found Automator's "Launch Application" action to be as quick as anything else, and the only way to do this without third party software.

BetterTouchTool is a free application that can be used to launch applications using hotkeys.

iTerm 2 is a Terminal.app replacement that can be shown/hidden using a hotkey (if it's running).