This can be achieved by using an Automator service and assigning it a shortcut in the Keyboard System Preference pane:
- Launch Automator and select “Service” as the type of new workflow to create.
- Set the workflow to take “no input” in “all applications”.
- Drag a “Run program“ action from the “Utilities” category into the workflow, set it to the app you want to start via a keyboard shortcut.
- Save the service under a memorable name.
- Go to Keyboard Preferences → Shortcuts (in System Preferences, or chooses “Configure Services” from the “Services” submenu in the Apple menu).
- Select the “Services” category, locate your newly created service and assign it a shortcut (make sure it is checked to be active).
Voilà – you have a global keyboard shortcut to start your application. Rinse and repeat as needed. Note Automator services are pretty laggy when first started during a session, but reasonably responsive after that.