Apple - Can I create a shortcut to open a specific application on OS X?

Karabiner-Elements (10.12 and later)

Karabiner stopped working in 10.12 due to changes in the kernel architecture, and Karabiner was rewritten as Karabiner-Elements which uses a new JSON format for the configuration files.

You can now add a rule like this to karabiner.json (https://pqrs.org/osx/karabiner/json.html):

{
  "from": {
    "key_code": "t",
    "modifiers": {
      "mandatory": [
        "right_option"
      ]
    }
  },
  "to": [
    {
      "shell_command": "open -aterminal"
    }
  ],
  "type": "basic"
}

This makes a short press of the right command key open Emacs:

{
  "from": {
    "key_code": "right_command",
    "modifiers": {
      "optional": [
        "any"
      ]
    }
  },
  "to": [
    {
      "key_code": "right_command",
      "lazy": true
    }
  ],
  "to_if_alone": [
    {
      "shell_command": "open -aemacs"
    }
  ],
  "type": "basic"
}

Karabiner (10.11 and earlier)

Save a file like this as private.xml:

<?xml version="1.0"?>
<root>
  <vkopenurldef>
    <name>KeyCode::VK_OPEN_URL_Safari</name>
    <url>file:///Applications/Safari.app</url>
  </vkopenurldef>
  <vkopenurldef>
    <name>KeyCode::VK_OPEN_URL_iTunes</name>
    <url>file:///Applications/iTunes.app</url>
  </vkopenurldef>
  <vkopenurldef>
    <name>KeyCode::VK_OPEN_URL_EMACS</name>
    <url>file:///Applications/Emacs.app</url>
  </vkopenurldef>
  <item>
    <name>custom</name>
    <identifier>custom</identifier>
    <autogen>__KeyToKey__ KeyCode::F11, KeyCode::VK_OPEN_URL_Safari</autogen>

    <!-- change the right option key into an extra modifier key -->
    <autogen>__KeyToKey__ KeyCode::OPTION_R, KeyCode::VK_MODIFIER_EXTRA1</autogen>

    <autogen>__KeyToKey__ KeyCode::I, ModifierFlag::EXTRA1, KeyCode::VK_OPEN_URL_iTunes</autogen>

    <!-- make a short press of the right command open Emacs -->
    <autogen>__KeyOverlaidModifier__ KeyCode::COMMAND_R, KeyCode::COMMAND_R, KeyCode::VK_OPEN_URL_EMACS</autogen>
  </item>
</root>

Alfred 2

If you have bought the Powerpack for Alfred 2, you can create a workflow like this:

Hotkeys have a short delay by default, but you can reduce the delay by changing the "Trigger behaviour" option from "Simulate modifier keys released" to "Pass through modifier keys (Fastest)":

Automator services

Open Automator, select "Service" as the type of the document, change "Service receives" from "text" to "no input", add a "Launch Application" action, and save the service. Then assign a keyboard shortcut for the service from "System Preferences > Keyboard > Shortcuts > Services".

I don't recommend this option, because at least on my system, there is at best a delay of around half a second before an application is focused by a keyboard shortcut created using this method, and the delay is often even longer. There has also been a bug since 10.7 where the keyboard shortcuts for Automator services don't always work until you hover over the services menu from the menu bar. (Edit: it's now 8 years after I wrote this answer and the bug still hasn't been fixed.) Also the keyboard shortcuts for services are not available in some applications like Emacs.

Alfred

Alfred, in its Power Pack version, can map shortcuts to applications, among many other features.

I found Apptivate the easiest to use. You just select an application and you assign a global shortcut. That's it.